It is commonly believed that in confining vector-like gauge theories the center and chiral symmetry realizations are parametrically entangled, and if phase transitions occur, they must take place around the strong scale $Λ^{-1}$ of the gauge theory. We demonstrate that (non-thermal) vector-like theories formulated on ${\mathbb R}^{3} \times S^1$ where $S^1$ is a spatial circle exhibit new dynamical scales and new phenomena. There are chiral phase transitions taking place at $Λ^{-1}/N_c$ in the absence of any change in center symmetry. $Λ^{-1}/N_c$, invisible in (planar) perturbation theory, is also the scale where abelian versus non-abelian confinement regimes meet. Large $N_c$ volume independence (a working Eguchi-Kawai reduction) provides new insights and independently confirms the existence of these scales. We show that certain phases and scales are outside the reach of holographic (supergravity) modeling of QCD.
For the exploration of the phase diagram of QCD, effective Polyakov loop theories derived from lattice QCD provide a valuable tool in the heavy quark mass regime. In practice, the evaluation of these theories is complicated by the appearance of long-range and multipoint interaction terms. On the other hand, it is well known that for theories with such kind of interactions mean field approximations can be expected to yield reliable results. Here, we apply this framework to the critical endpoint of the deconfinement transition and results are compared to the literature. This treatment can also b…
QCD with a finite baryon chemical potential, despite its importance, is not well understood because the standard lattice QCD simulation is not applicable due to the sign problem. Although sign-free QCD-like theories have been studied intensively, relation to QCD with a finite baryon chemical potential was not clear until recently. In this talk we explain the large-Nc equivalences between QCD and various QCD-like theories, which lead us to a unified viewpoint for QCD with baryon and isospin chemical potentials, SO(2Nc) and Sp(2Nc) gauge theories. In particular two-flavor QCD with the baryon che…
We argue that the whole or the part of the phase diagrams of QCD and QCD-like theories should be universal in the large-N_c limit through the orbifold equivalence. The whole phase diagrams, including the chiral phase transitions and the BEC-BCS crossover regions, are identical between SU(N_c) QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon chemical potential. Outside the BEC-BCS crossover region in these theories, the phase diagrams are also identical to that of SU(N_c) QCD at finite baryon chemical potential. We give examples of the universal…
We show the universality of phase diagrams in QCD and QCD-like theories through the large-N_c equivalence. The whole phase diagrams are identical between QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon chemical potential. In the chiral limit, they are also identical to that of QCD at finite chiral chemical potential. Outside the pion or diquark condensed phase in these theories, the universality of phase diagrams is applicable to QCD at finite baryon chemical potential. We further argue that the universality may work approximately even for N_c…
Volume independence in large $\Nc$ gauge theories may be viewed as a generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai reduction) is a special case of this equivalence. So is temperature independence in confining phases. In pure Yang-Mills theory, the failure of volume independence for sufficiently small volumes (at weak coupling) due to spontaneous breaking of center symmetry, together with its validity above a critical size, nicely illustrate the symmetry realization conditions which are both necessary and sufficient for large $\Nc$ orbifold equivalence. The exi…
The Yang-Mills gradient flow for QCD-like theories is generalized by including a fermionic matter term in the gauge field flow equation. We combine this with two different flow equations for the fermionic degrees of freedom. The solutions for the different gradient flow setups are used in the perturbative computations of the vacuum expectation value of the Yang-Mills Lagrangian density and the field renormalization factor of the evolved fermions up to next-to-leading order in the coupling. We find a one-parameter family of flow systems for which there exists a renormalization scheme in which t…
The dynamics with an infrared stable fixed point in the conformal window in QCD like theories with a relatively large number of fermion flavors is reviewed. The emphasis is on the description of a clear signature for the conformal window, which in particular can be useful for lattice computer simulations of these gauge theories.
In these lectures I review some basic examples of how the concepts of universality and scaling can be used to study aspects of the chiral and the deconfinement transition, if not in QCD directly but in QCD-like theories. As an example for flavor dynamics I discuss a quark-hadron model to describe the phase diagram of two-color QCD with the functional renormalization group. Universal aspects of deconfinement are illustrated mainly in the 2+1 dimensional SU(N) gauge theories with second order transition where many exact results from spin models can be exploited.
The dynamics with an infrared stable fixed point in the conformal window in QCD like theories (with a relatively large number of fermion flavors) is studied. The dependence of masses of colorless bound states on a bare fermion mass is described. In particular it is shown that in such dynamics, glueballs are much lighter than bound states composed of fermions, if the value of the infrared fixed point is not too large. This yields a clear signature for the conformal window, which is in particular can be useful for lattice computer simulations of these gauge theories.
We study the phase diagrams of $\Nc= \infty$ vector-like, asymptotically free gauge theories as a function of volume, on $S^3\times S^1$. The theories of interest are the ones with fermions in two index representations [adjoint, (anti)symmetric, and bifundamental abbreviated as QCD(adj), QCD(AS/S) and QCD(BF)], and are interrelated via orbifold or orientifold projections. The phase diagrams reveal interesting phenomena such as disentangled realizations of chiral and center symmetry, confinement without chiral symmetry breaking, zero temperature chiral transitions, and in some cases, exotic pha…
We investigate the universality of truncation schemes for Dyson-Schwinger equations developed for quantum chromodynamics in theories which differ from quantum chromodynamics only in the gauge group. Our specific choices are the gauge groups $SU(2)$ and $G_2$, for which lattice calculations at nonvanishing chemical potential are possible. Thus, corresponding calculations can provide benchmarks for testing calculations with functional equations. We calculate the quark and gluon propagators and determine the chiral and dual chiral condensates at vanishing density to determine the confinement/deco…
Deep insights into the possible infrared dynamics of strongly-coupled nonAbelian gauge theories such as QCD come from the analyses of ${\cal N}=1$ or ${\cal N}=2$ supersymmetric gauge theories. Central in the whole discussion will be the topological soliton monopoles and vortices and their quantum dynamics. We review the arguments that nonAbelian monopoles, free from the classic "difficulties", can be defined semi-classically via the topology and stability connection to the better understood nonAbelian vortices. Recent results on $CP^{N-1}$ models on $2D$ worldsheet of finite width, establish …
Much about the confinement and dynamical symmetry breaking in QCD might be learned from models with supersymmetry. In particular, models based on N=2 supersymmetric theories with gauge groups SU(N), SO(N) and $USp(2 N)$ and with various number of flavors, give deep dynamical hints about these phenomena. For instance, the BPS non-abelian monopoles can become the dominant degrees of freedom in the infrared due to quantum effects. Upon condensation (which can be triggered in these class of models by perturbing them with an adjoint scalar mass) they induce confinement with calculable pattern of dy…
QCD with a finite baryon chemical potential, despite its importance, is not well understood because the standard lattice QCD simulation is not applicable due to the sign problem. Although QCD-like theories which do not suffer from the sign problem have been studied intensively, relation to QCD with a finite baryon chemical potential was not clear. This paper introduces large-$N_c$ equivalences between QCD and various QCD-like theories. These equivalences lead us to a unified viewpoint for QCD with baryon and isospin chemical potentials, $SO(2N_c)$ and $Sp(2N_c)$ gauge theories, QCD with adjoin…
We use 2-color QCD as a model to study the effects of simultaneous presence of chemical potentials for isospin charge, $μ_I$, and for baryon number, $μ_B$. We determine the phase diagrams for 2 and 4 flavor theories using the method of effective chiral Lagrangians at low densities and weak coupling perturbation theory at high densities. We determine the values of various condensates and densities as well as the spectrum of excitations as functions of $μ_I$ and $μ_B$. A similar analysis of QCD with quarks in the adjoint representation is also presented. Our results can be of relevance for latti…
Recent work on QCD-like theories on R^3 x S^1 has revealed that a confined phase can exist when the circumference L of S^1 is sufficiently small. Adjoint QCD and double-trace deformation theories with certain conditions are such theories, and we present some new results for their phase diagrams. First we show the connection between the large-L and small-L confined regions in the phase diagram of SU(3) adjoint QCD using Polyakov-Nambu-Jona Lasinio models. Then we consider an SU(2) double-trace deformation theory with adjoint scalars and study conflicts between the Higgs and small-L confined pha…
These are the proceedings of the workshop on ``Effective Field Theories of QCD'' held at the Physikzentrum Bad Honnef of the Deutsche Physikalische Gesellschaft, Bad Honnef, Germany from November 26 to 30, 2001. The workshop concentrated on Chiral Perturbation Theory in its various settings, its relations with lattice QCD and dispersion theory and the use of effective field theories in systems with one, two or more nucleons as well as at high baryon densities. Included are a short contribution per talk and a listing of some review papers on the subject.
It is shown that, in some non-QCD theories, there are effects shared by QCD: (i)~in SU(2) Yang-Mills theory containing a nonlinear spinor field, there is a mass gap; (ii)~in SU(3) Proca-Higgs theory, there are flux tube solutions with a longitudinal electric field required for producing a force binding quarks; (iii)~in non-Abelian Proca-Higgs theories, there exist flux tube solutions with a momentum directed along the tube axis and particlelike solutions with a nonvanishing total angular momentum created by crossed color electric and magnetic fields; in QCD, such configurations may contribute …
Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R^3 x S^1 can be studied via a unitary matrix quantum mechanics on S^1, by varying the temperature. To confirm this no…
Massive QCD at $θ=π$ breaks CP spontaneously and admits domain walls whose dynamics and phases depend on the number of flavors and their masses. We discuss these issues within the Witten-Sakai-Sugimoto model of holographic QCD. Besides showing that this model reproduces all QCD expectations, we address two interesting claims in the literature. The first is about the possibility that the QCD domain-wall theory is fully captured by three-dimensional physics, only. The second regards the existence of quantum phases in certain Chern-Simons theories coupled to fundamental matter. Both claims are su…
A construction of master field describing multicolour QCD is presented. The master fields for large N matrix theories satisfy to standard equations of relativistic field theory but fields are quantized according $q$-deformed commutation relations with $q=0$. These commutation relations are realized in the Boltzmannian Fock space. The master field for gauge theory does not take values in a finite-dimensional Lie algebra, however, there is a non-Abelian gauge symmetry and BRST-invariance.
Exotic states have been predicted before and after the advent of QCD. In the last decades they have been observed at accelerator experiments in the sector with two heavy quarks, at or above the quarkonium strong decay threshold and called X Y Z states. These states offer a unique possibility for investigating the dynamical properties of strongly correlated systems in QCD. I will show how an alliance of nonrelativistic effective field theories and lattice can allow us to address these states in QCD. In particular I will explain what are the opportunities and challenges of lattice QCD in this re…
We review the present status of the Anderson transition in the spectrum of the Dirac operator of QCD-like theories on the lattice. Localized modes at the low-end of the spectrum have been found in SU(2) Yang-Mills theory with overlap and staggered valence fermions as well as in Nf=2+1 QCD with staggered quarks. We draw an analogy between the transition from localized to delocalized modes in the Dirac spectrum and the Anderson transition in electronic systems. The QCD transition turns out to be in the same universality class as the transition in the corresponding Anderson model. We also specula…
We are able to show that BF theories naturally emerge from the coadjoint orbits of $W_2$ and $w_\infty$ algebras which includes a Kac-Moody sector. Since QCD strings can be identified with a BF theory, we are able to show a relationship between the orbits and monopole-string solutions of QCD. Furthermore, we observe that when 4D gravitation is cast into a BF form through the use of Ashtekar variables, we are able to get order $\hbar$ contributions to gravity which can be associated with the $W_2$ anomaly. We comment on the relationship to gravitational monopoles.
Yang-Mills theories with a gauge group SU(N_c\=3)and quark matter in the fundamental representation share many properties with the theory of strong interactions, QCD with N_c=3. We show that, for N_c even and in the confinement phase, the gluonic average of the quark determinant is independent of the boundary conditions, periodic or anti-periodic ones. We then argue that a Fermi sphere of quarks can only exist under extreme conditions when the centre symmetry is spontaneously broken and colour is liberated. Our findings are supported by lattice gauge simulations for N_c=2...5 and are illustrat…
We analyze the smallest Dirac eigenvalues by formulating an effective theory for the QCD Dirac spectrum. We find that in a domain where the kinetic term of the effective theory can be ignored, the Dirac eigenvalues are distributed according to a Random Matrix Theory with the global symmetries of the QCD partition function. The kinetic term provides information on the slope of the average spectral density of the Dirac operator. In the second half of this lecture we interpret quenched QCD Dirac spectra at nonzero chemical potential (with eigenvalues scattered in the complex plane) in terms of an…
A previous analysis of possible constraints of Yang-Mills instantons in the presence of spontaneous symmetry breaking is extended to supersymmetric QCD. It is again found that a constraint is necessary for the gauge field in second and fourth order of the gauge breaking parameter v. While the supersymmetric zero mode is well behaved to all orders, the lifted superconformal and quark zero modes show nonpermissible behaviour, but only at first order in v.
We study QCD-like theories with pseudoreal fermions at finite baryon density. Such theories include two-color QCD with quarks in the fundamental representation of the color group as well as any-color QCD with quarks in the adjoint color representation. In all such theories the lightest baryons are diquarks. At zero chemical potential $μ$ they are, together with the pseudoscalar mesons, the Goldstone modes of a spontaneously broken enlarged chiral symmetry group. Using symmetry principles, we derive the low-energy effective Lagrangian for these particles. We find that a second order phase trans…
We consider QCD-like theories with one massless fermion in various representations of the gauge group SU$(N)$. The theories are formulated on $R_3\times S_1$. In the decompactification limit of large $r(S_1)$ all these theories are characterized by confinement, mass gap and spontaneous breaking of a (discrete) chiral symmetry ($χ$SB). At small $r(S_1)$, in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double trace deformation. With these deformation, the theories at hand are at weak coupling at small $r(S_1)$ and yet exhibit basic features …
Gauge theories with gauge group $SU(N)$ and quarks belonging to arbitrary representations of $SU(N)$ form a rich landscape of QCD-like theories, whose study can shed new light on the properties of confinement. Four cases are particularly worth of interest: quarks in the fundamental representation, quarks in the 2-indice (anti)symmetric representation and quarks in the adjoint representation. The last three corresponding QCD-like theories are equivalent at large-$N$ for bosonic observables: It is the orientifold equivalence. The behavior of the lightest vector meson mass versus $N$ has been stu…
We derive the necessary and sufficient conditions for a 2d QCD theory of massless gluons and left and right chiral quarks in arbitrary representations of a gauge group G to develop a mass gap. These results are obtained from spectral properties of the lightcone and temporal QCD Hamiltonians. The conditions can be explicitly solved, and we provide the complete list of all 2d QCD theories that have a quantum mechanical gap in the spectrum, while any other theory not in the list is gapless. The list of gapped theories includes QCD models with quarks in vector-like as well as chiral representation…
It is shown that in vector-like gauge theories, such as QCD, and in the limit of a large number of colours Nc, the ordering pattern of narrow vector and axial-vector states at low energies is correlated with the size of the possible local order parameters of chiral symmetry breaking. This has implications on the underlying dynamics of spontaneous chiral symmetry breaking in QCD, and also on possible values of the parameter S for oblique electroweak corrections, the analogue of the QCD low energy constant L10.
We study the global symmetries of naive lattices Dirac operators in QCD-like theories in any dimension larger than two. In particular we investigate how the chosen number of lattice sites in each direction affects the global symmetries of the Dirac operator. These symmetries are important since they do not only determine the infra-red spectrum of the Dirac operator but also the symmetry breaking pattern and, thus, the lightest pseudo-scalar mesons. We perform the symmetry analysis and discuss the possible zero modes and the degree of degeneracy of the lattice Dirac operators. Moreover we expli…
This paper is a continuation of ArXiv:0707.1324 where improved holographic theories for QCD were set up and explored. Here, the IR confining geometries are classified and analyzed. They all end in a "good" (repulsive) singularity in the IR. The glueball spectra are gaped and discrete, and they favorably compare to the lattice data. Quite generally, confinement and discrete spectra imply each other. Asymptotically linear glueball masses can also be achieved. Asymptotic mass ratios of various glueballs with different spin also turn out to be universal. Mesons dynamics is implemented via space fi…
In the last twenty years, low-energy (IR) dualities have been found for many pairs of supersymmetric gauge theories with four supercharges, both in four space-time dimensions and in three space-time dimensions. In particular, duals have been found for 3d N=2 supersymmetric QCD theories with gauge group U(N), with F chiral multiplets in the fundamental representation, with F' chiral multiplets in the anti-fundamental representation, and with Chern-Simons level k, for all values of N, F, F' and k for which the theory preserves supersymmetry. For SU(N) theories the duals have been found in some c…
We present analytical results for the Euclidean 2-point correlator of the flavor-singlet vector current evolved by the gradient flow at next-to-leading order ($O(g^2)$) in perturbatively massless QCD-like theories. We show that the evolved 2-point correlator requires multiplicative renormalization, in contrast to the nonevolved case, and confirm, in agreement with other results in the literature, that such renormalization ought to be identified with a universal renormalization of the evolved elementary fermion field in all evolved fermion-bilinear currents, whereas the gauge coupling renormali…
A review is given of recent research on two-dimensional gauge theories, with particular emphasis on the equivalence between these theories and certain string theories with a two-dimensional target space. Some related open problems are discussed.
We introduce Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories. We show that they are equivalent to the $ε$-limit of the chiral Lagrangian for Wilson chiral perturbation theory. Results are obtained for two-color QCD with quarks in the fundamental representation of the color group as well as any-color QCD with quarks in the adjoint representation. For $N_c=2$ we also have obtained the lattice spacing dependence of the quenched average spectral density for a fixed value of the index of the Dirac operator. Comparisons with direct numerical simulations of the rando…
We derive the sum rule for the spectral function of the stress-energy tensor in the bulk (uniform dilatation) channel in a general class of strongly coupled field theories. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly. In the limit when the operator becomes marginal, the sum rule coincides with that in QCD. Using the holographic model, we verify explicitly the cancellation between large and small frequency contributions to the spectral integral required to satisfy the sum rule in such Q…
We calculate the relativistic six-meson scattering amplitude at low energy within the framework of QCD-like theories with $n$ degenerate quark flavors at next-to-leading order in the chiral counting. We discuss the cases of complex, real and pseudo-real representations, i.e. with global symmetry and breaking patterns $\text{SU}(n)\times\text{SU}(n)/\text{SU}(n)$ (extending the QCD case), $\text{SU}(2n)/\text{SO}(2n)$, and $\text{SU}(2n)/\text{Sp}(2n)$. In case of the one-particle-irreducible part, we obtain analytical expressions in terms of 10 six-meson subamplitudes based on the flavor and g…
Various holographic approaches to QCD in five dimensions are explored using input both from the putative non-critical string theory as well as QCD. It is argued that a gravity theory in five dimensions coupled to a dilaton and an axion may capture the important qualitative features of pure QCD. A part of the higher alpha' corrections are resummed into a dilaton potential. The potential is shown to be in one-to-one correspondence with the exact beta-function of QCD, and its knowledge determines the full structure of the vacuum solution. The geometry near the UV boundary is that of AdS_5 with lo…
We introduce a new concept "conformal theories with an IR cutoff", after pointing out that the following two categories in SU(3) gauge theories with fundamental N_f fermions possess an IR fixed point: Large N_f QCD with N_f in the conformal window (referred as Conformal QCD) and small N_f QCD with N_f out of the conformal window at temperature T/Tc > 1 (referred as High Temperature QCD). In the conformal theories with an IR cutoff there exists the "conformal region'" together with the confining region and the deconfining region. We verify numerically on a lattice of the size 16^3 x64 the exist…
We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark condensate, in contrast to the complex Dirac eigenvalues whose scale is set by the chiral condensate at low density and by the BCS gap at high density. We identify three different low-energy effective theories with diquark sources applicable at low, intermediate, and high density, together with their overlapping domains of validity. We derive a number of exact formula…
We analyze Dirac spectra of two-dimensional QCD like theories both in the continuum and on the lattice and classify them according to random matrix theories sharing the same global symmetries. The classification is different from QCD in four dimensions because the anti-unitary symmetries do not commute with $γ_5$. Therefore in a chiral basis, the number of degrees of freedom per matrix element are not given by the Dyson index. Our predictions are confirmed by Dirac spectra from quenched lattice simulations for QCD with two or three colors with quarks in the fundamental representation as well a…
In this chapter of the Oxford Handbook of Random Matrix Theory we introduce chiral Random Matrix Theories with the global symmetries of QCD. In the microscopic domain, these theories reproduce the mass and chemical potential dependence of QCD. The main focus of this chapter is on the spectral properties of the QCD Dirac operator and relations between chiral Random Matrix Theories and chiral Lagrangians. Both spectra of the anti-hermitian Dirac operator and spectra of the nonhermitian Dirac operator at nonzero chemical potential are discussed.
We study a number of different ingredients, related to long range order observed in lattice QCD simulations, using a simple "deformed QCD" model. This model is a weakly coupled gauge theory, which however has all the relevant crucial elements allowing us to study difficult and nontrivial problems which are known to be present in real strongly coupled QCD. In the present study, we want to understand the physics of long range order in form of coherent low dimensional vacuum configurations observed in Monte Carlo lattice simulations. We demonstrate the presence of double-layer domain wall structu…
The 't Hooft and Corrigan-Ramond limits of massless one-flavor QCD consider the two Weyl fermions to be respectively in the fundamental representation or the two index antisymmetric representation of the gauge group. We introduce a limit in which one of the two Weyl fermions is in the fundamental representation and the other in the two index antisymmetric representation of a generic SU(N) gauge group. This theory is chiral and to avoid gauge anomalies a more complicated chiral theory is needed. This is the generalized Georgi-Glashow model with one vector like fermion. We show that there is an …
We present a simple AdS/QCD model in which the formation of the chiral condensate is dynamically determined. The gauge dynamics is input through the running of the quark bilinear's anomalous dimension, gamma. The condensate provides a dynamically generated infra-red wall in the computation of mesonic bound state masses and decay constants. As an example, we use the model, with perturbative computations of the running of gamma, to study SU(3) gauge theory with a continuous number of quark flavours, Nf. We follow the behaviour of the spectrum as we approach the conformal window through a walking…
We present a method for extracting effective Lagrangians from QCD. The resulting effective Lagrangians are based on exact rewrites of cut-off QCD in terms of these new collective field degrees of freedom. These cut-off Lagrangians are thus ``effective'' in the sense that they explicitly contain some of the physical long-distance degrees of freedom from the outset. As an example we discuss the introduction of a new collective field carrying the quantum numbers of the $η'$-meson. (Contribution presented by R. Sollacher at the workshop ``QCD'94'', Montpellier, France, July 7-13, 1994. To appear i…
I present a set of theories which display non-trivial `t Hooft anomaly matching for QCD with $F$ flavors. The matching theories are non-Abelian gauge theories with "dual" quarks and baryons, rather than the purely confining theories of baryons that `t Hooft originally searched for. The matching gauge groups are required to have an $F\pm 6$ dimensional representation. Such a correspondence is reminiscent of Seiberg's duality for supersymmetric (SUSY) QCD, and these theories are candidates for non-SUSY duality. However anomaly matching by itself is not sufficiently restrictive, and duality for Q…
In non-Hermitian random matrix theory there are three universality classes for local spectral correlations: the Ginibre class and the nonstandard classes $\mathrm{AI}^\dagger$ and $\mathrm{AII}^\dagger$. We show that the continuum Dirac operator in two-color QCD coupled to a chiral $\mathrm{U}(1)$ gauge field or an imaginary chiral chemical potential falls in class $\mathrm{AI}^\dagger$ ($\mathrm{AII}^\dagger$) for fermions in pseudoreal (real) representations of $\mathrm{SU}(2)$. We introduce the corresponding chiral random matrix theories and verify our predictions in lattice simulations wit…
Dependence of the confinement transition parameters on the fermion content provides information on the mechanism of confinement. Recent progress in lattice gauge theories has allowed to study it for light flavor number $N_f\sim O(10)$ and found this transition to shift toward significantly stronger coupling. We propose an explanation for that: light fermions can occupy the chromo-magnetic monopoles, via zero modes, making them "distinguishable" and unsuitable for Bose-Einstein Condensation. Such dilution of unoccuplied monopoles is compensated by stronger coupling that makes them lighter and m…
We suggest a tetracritical fixed point to naturally occur in strongly interacting theories. As a fundamental example we analyze the temperature--quark chemical potential phase diagram of QCD with fermions in the adjoint representation of the gauge group (i.e. adjoint QCD). Here we show that such a non trivial multicritical point exists and is due to the interplay between the spontaneous breaking of a global U(1) symmetry and the center group symmetry associated to confinement. Our results demonstrate that taking confinement into account is essential for understanding the critical behavior as w…
We analyze the Coulomb phase of theories of $N=2$ SQCD with $SU(N_c)$ gauge groups which are conjectured to have exact electric-magnetic duality. We discuss the duality transformation of the particle spectrum, emphasizing the differences between the general case and the $SU(2)$ case. Some difficulties associated with the definition of the duality transformation for a general gauge group are discussed. We compute the classical monopole spectrum of these theories, and when it is possible we use it to check the consistency of the duality. Generally these theories may have phase transitions betwee…
I propose a controlled approximation to QCD-like theories with massless quarks by employing supersymmetric QCD perturbed by anomaly-mediated supersymmetry breaking. They have identical massless particle contents. Thanks to the ultraviolet-insensitivity of anomaly mediation, dynamics can be worked out exactly when $m \ll Λ$, where $m$ is the size of supersymmetry breaking and $Λ$ the dynamical scale of the gauge theory. I demonstrate that chiral symmetry is dynamically broken for $N_{f} \leq \frac{3}{2} N_{c}$ while the theories lead to non-trivial infrared fixed points for larger number of fla…
We evaluate the induced value of Newton's constant which would arise in QCD. The ingredients are modern lattice results, perturbation theory and the operator product expansion. The resulting shift in the Planck mass is positive. A scaled-up version of such a theory may be part of a quantum field theory treatment of gravity.
Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds the promise to address currently unsolvable problems, such as the real-time and high-density dynamics of strongly interacting matter, first in toy-model gauge theories, and ultimately in QCD.
Recent works argue that the pattern of chiral symmetry breaking in QCD-like theories can be derived from supersymmetric (SUSY) QCD with perturbation of anomaly-mediated SUSY breaking (AMSB). Nevertheless, despite the fact that AMSB needs to be a small (but still exact) perturbation, there are two other major problems remaining unsolved: first, in order to derive the chiral symmetry breaking pattern, one needs to minimize the potential along a certain specific direction, identifying this direction fully as an outcome is nontrivial given the moduli space of degenerate vacua in the SUSY limit; se…
