By superposition of regular gauge instantons or merons, ensembles of gauge fields are constructed which describe the confining phase of SU(2) Yang-Mills theory. Various properties of the Wilson loops, the gluon condensate and the topological susceptibility are found to be in qualitative agreement with phenomenology or results of lattice calculations. Limitations in the application to the glueball spectrum and small size Wilson loops are discussed.
We discuss a confining model for quark-antiquark system with a new color $SU_3$ gauge symmetry. New gauge transformations involve non-integrable phase factors and lead to the fourth-order gauge field equations and a linear potential. The massless gauge bosons have non-definite energies, which are not observable because they are permanently confined in quark systems by the linear potential. We use the empirical potentials of charmonium to determine the coupling strength of the color charge $g_s$ and find $g_s^2/(4π) \approx 0.2.$ We discuss Feynman-Dyson rules for the confining quark model, whi…
We discuss a confining model for charmonium in which the attractive force are derived from a new type of gauge field equation with a generalized $SU_3$ gauge symmetry. The new gauge transformations involve non-integrable phase factors with vector gauge functions $\om^a_μ(x)$. These transformations reduce to the usual $SU_3$ gauge transformations in the special case $\om^a_μ(x) = \p_μξ^a(x)$. Such a generalized gauge symmetry leads to the fourth-order equations for new gauge fields and to the linear confining potentials. The fourth-order field equation implies that the corresponding massless ga…
We study chiral symmetry breaking in QCD-like gauge theories introducing a confining effective propagator, as proposed recently by Cornwall, and considering the effect of dynamical gauge boson mass generation. The effective confining propagator has the form $1/(k^2+m^2)^2$ and we study the bifurcation equation finding limits on $m$ below which a satisfactory fermion mass solution is generated. Since the coupling constant and gauge boson propagator are damped in the infrared, due to the presence of dynamically massive gauge bosons, the major part of the chiral breaking is only due to the confin…
$Q\bar{Q}$ potential is studied in the SU(2) gauge theory. Based on the nonlinear gauge of the Curci-Ferrari type, the possibility of a gluon condensation $\langle A_μ^+A_μ^-\rangle$ in low-energy region has been considered at the one-loop level. Instead of the magnetic monopole condensation, this condensation makes classical gluons massive, and can yield a linear potential. We show this potential consists of the Coulomb plus linear part and an additional part. Comparing with the Cornell potential, we study this confining potential in detail, and find that the potential has two implicit scales…
In this paper we study the breaking of chiral symmetry with non-confining power-like potentials. The region of allowed exponents is identified and, after the previous study of confining (positive exponent) potentials, we now specialize in shorter range non-confining potentials, with a negative exponent. These non-confining potentials are close to the Coulomb potential, and they are also relevant as corrections to the linear confinement, and as models for the quark potential at the deconfinement transition. The mass-gap equation is constructed and solved, and the quarks mass, the chiral angle a…
We consider a charged scalar particle $χ$ of mass around 375 GeV charged under both $SU(3)_c$ and a new confining non-abelian gauge interaction. After pair production, these interactions confine the exotic scalar into non-relativistic bound states whose decays into photons can explain the 750 GeV diphoton excess observed at the LHC. Taking the new confining group to be $\mathrm{SU}(2)$, we find $χ$ must carry an electric charge of $Q \sim [\frac{1}{2}, 1]$ to fit the data. Interestingly, we find that pair production of the scalars and the subsequent formation of the bound state dominates over …
We examine N=1 supersymmetric gauge theories which confine in the presence of a tree-level superpotential. We show the confining spectra which satisfy the 't Hooft anomaly matching conditions and give a simple method to find the confining superpotential. Using this method we fix the confining superpotentials in the simplest cases, and show how these superpotentials are generated by multi-instanton effects in the dual theory. These new type of confining theories may be useful for model building, since the size of the matter content is not restricted by an index constraint. Therefore, one expect…
Four-dimensional asymptotically-free large $N$ gauge theories compactified on $S^3_R \times \mathbb{R}$ have a weakly-coupled confining regime when $R$ is small compared to the strong scale. We compute the vacuum energy of a variety of confining large $N$ non-supersymmetric gauge theories in this calculable regime, where the vacuum energy can be thought of as the $S^3$ Casimir energy. The $N=\infty$ renormalized vacuum energy turns out to vanish in all of the large $N$ gauge theories we have examined, confirming a striking prediction of temperature-reflection symmetry.
We show that theories in the confining, free magnetic, and conformal phases can break supersymmetry through dynamical effects. To illustrate this, we present theories based on the gauge groups $SU(n)\times SU(4)\times U(1)$ and $SU(n) \times SU(5) \times U(1)$ with the field content obtained by decomposing an $SU(m)$ theory with an antisymmetric tensor and $m-4$ antifundamentals.
We present a numerical method to compute path integrals in effective SU(2) Yang-Mills theories. The basic idea is to approximate the Yang-Mills path integral by summing over all gauge field configurations, which can be represented as a linear superposition of a small number of localized building blocks. With a suitable choice of building blocks many essential features of SU(2) Yang-Mills theory can be reproduced, particularly confinement. The analysis of our results leads to the conclusion that topological charge as well as extended structures are essential elements of confining gauge field co…
Properties of extra weak bosons are discussed in a gauge model based on SU(2)_LXU(1)_YXSU(2)'_L. The physics of SU(2)'_L respects the duality in the Higgs and confining phases, where massive gauge bosons in the Higgs phase are equivalently represented by composite vector bosons in the confining phase below the scale of SU(2)'_L . interactions for SU(2)'_L-singlet composites induced in the confining phase can be generated by nonlinear interactions of the four Fermi type respecting SU(2)_LXU(1)_Y, which create quarks, q_i^A (A=r,g,b; i=1,2), leptons, l_i, vector bosons, V_mu^(a) (a=1,2,3) and th…
We consider the phase structure of a pure compact U(1) gauge theory in four dimensions at finite temperature by treating this system as a perturbative deformation of the topological model. Phases of a gauge theory can be investigated from the phase structure of the topological model. The thermal pressure of the topological model has been calculated, from which its phase structure can be derived. We have obtained phases of a compact U(1) gauge theory. Moreover, the critical-line equation has been explicitly evaluated.
The structure of the Abelian-projected (AP) flux tube in SU(2) gauge theory in the maximally Abelian gauge is studied by applying the Hodge decomposition to the Abelian Wilson loop. It is shown that the profile of the AP flux tube has the same structure as the classical flux tube solution in the dual Abelian Higgs model, which is composed of a Coulombic and a solenoidal electric field linked by monopole supercurrent.
The pseudoparticle approach is a numerical method to approximate path integrals in SU(2) Yang-Mills theory. Path integrals are computed by summing over all gauge field configurations, which can be represented by a linear superposition of a small number of pseudoparticles with amplitudes and color orientations as degrees of freedom. By comparing different pseudoparticle ensembles we determine properties of confining gauge field configurations. Our results indicate the importance of long range interactions between pseudoparticles and of non trivial topological properties.
We present an analytic nonperturbative solution of the Yakubovsky equation for tetraquark states in the case of equal separations and energies, and demonstrate a direct connection between the tetraquark confinement potential and the temporal gluon propagator. To this end we employ a leading-order heavy quark mass expansion of the Coulomb gauge QCD action, and use the dressed two-point functions of the Yang-Mills sector only. As a result we find a bound state energy that rises linear with distance and a string tension twice as large as in a $q\bar{q}$-system.
The Coulomb gauge model of QCD is studied with the introduction of a confining potential into the scalar part of the vector potential. Using a Green function formalism, we derive the self-energy for this model, which has both scalar and vector parts, $Σ^S(p)$ and $Σ^V(p)$. A rotation of these variables leads to the so-called gap and energy equations. We then analyse the divergence structure of these equations. As this depends explicitly on the form of potential, we give as examples both the linear plus Coulomb and quadratically confining potentials. The nature of the confining single particle …
The light quark propagation in the confining vacuum, described by an (infinite) set of gauge-invariant vacuum correlators, is studied in detail. To keep gauge invariance at each step the system of light quark and heavy antiquark is considered, and the nonlinear equations are written explicitly for the quark propagator in the limit of large $N_c$. For the lowest (Gaussian) correlator the system is studied in various approximations, and the relativistic WKB method is used to demonstrate the scalar confining interaction of light quarks, which implies chiral symmetry breaking. The chiral condensat…
We explain the recent diphoton excesses around $750$ GeV by both ATLAS and CMS as a singlet scalar $Φ$ which couples to SM gluon and neutral gauge bosons only through higher dimensional operators. A natural explanation is that $Φ$ is a pseudo-Nambu-Goldstone boson (pNGB) which receives parity violation through anomaly if there exists a hidden strong dynamics. The singlet and other light pNGBs will decay into two SM gauge bosons and even serves as the meta-stable coloured states which can be probed in the future. By accurately measuring their relative decay and the total production rate in the …
We explore the possible low energy phases of the confining non-supersymmetric $SU(5)$ chiral gauge theory with three generations of fermions in the $(10+\bar{5})$ representations. This theory has the same fermion and gauge matter content as the simplest Georgi-Glashow grand unified theory of the Standard Model and has an $SU(3)\times SU(3)\times U(1)$ global symmetry. Using 't Hooft anomaly matching, most attractive channel, and soft SUSY breaking approaches, we outline a number of possible consistent low energy vacua including one with a remnant $SO(3)\times U(1)$ symmetry that is analogous t…
Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTokyo Institutes for Advanced Study, University of Tokyo（东京大学UTokyo高等研究院Kavli宇宙物理与数学研究所）；Department of Physics, University of California, Berkeley（加州大学伯克利分校物理系）；Theoretical Physics Group, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室理论物理组）
We study the gauge boson propagator in the dual Abelian Higgs theory which confines electric charges. The confinement is due to dual Abrikosov-Nielsen-Olesen strings. We show that the infrared double pole 1/(p^2)^2 in the propagator is absent due to the confinement phenomenon. Instead, specific angular singularities signal the eventual set in of the confinement. These angular singularities are a manifestation of the confining strings.
We analyze the leading Lyapunov exponents of SU(2) Yang-Mills field configurations on the lattice which are initialized by quantum Monte Carlo simulations. We find that configurations in the strong coupling phase at finite temperature are substantially more chaotic than in deconfinement.
The Dyson-Schwinger equations arising from minimizing the vacuum energy density in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge are solved numerically. A new solution is presented which gives rise to a strictly linearly rising static quark potential and whose existence was previously observed in the infrared analysis of the Dyson-Schwinger equations. For the new solution we also present the static quark potential and calculate the running coupling constant from the ghost-gluon vertex.
We consider the soft wall model for a heuristic holographical modelling of a confining gauge theory and discuss how the introduction of a (constant) magnetic field influences the (de)confinement phase structure. We use the entanglement entropy as a diagnostic tool in terms of the length of an entangling strip geometry. Due to the anisotropy introduced by the magnetic field, we find that the results depend on the orientation of the strip relative to the field. This allows to identify a richer, anisotropic, interplay between confinement and a magnetic field than possibly can be extracted from a …
We discuss the transformation of the QCD temporal-gauge Hamiltonian to a representation in which it can be expressed as a functional of gauge-invariant quark and gluon fields. We show how this objective can be realized by implementing the non-Abelian Gauss's law, and by using the mathematical apparatus developed for that purpose to also construct gauge-invariant quark and gluon fields. We demonstrate that, in the transformed QCD Hamiltonian, the interactions of pure-gauge components of the gauge field with color-current densities are replaced by nonlocal interactions connecting quark color-cha…
The emergence of flux-tubes as the distance is increased between a quark and an antiquark is explored in a three-dimensional confining gauge theory using the gauge/gravity duality. We delineate the shape of the flux-tube corresponding to the classical open string in the bulk and further explore the fluctuation in its thickness induced by the fluctuation of the open string along the radial direction in the bulk. The relationship between the intrinsic shape of a flux-tube and its effect on the heavy quark potential is also discussed.
This is the content of a set of lectures given at the XIII Jorge Andre Swieca Summer School on Particles and Fields, held in Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the diffe…
Confining strings in 4D are effective, thick strings describing the confinement phase of compact U(1) and, possibly, also non-Abelian gauge fields. We show that these strings are dual to the gauge fields, inasmuch as their perturbative regime corresponds to the strong coupling (large e) regime of the gauge theory. In this regime they describe smooth surfaces with long-range correlations and Hausdorff dimension two. For lower couplings e and monopole fugacities z, a phase transition takes place, beyond which the smooth string picture is lost. On the critical line intrinsic distances on the surf…
We show that new nonperturbative scales exist in four-dimensional ${\cal{N}}$$=$$1$ super-Yang-Mills theory compactified on a circle, with an iterated-exponential dependence on the inverse gauge coupling. The lightest states with the quantum numbers of four-dimensional glueballs are nonrelativistic bound states of dual Cartan gluons and superpartners, with binding energy equal to $e^{- e^{1/g^2}}$ in units of the confining mass gap. Focusing on $SU(2)$ gauge group, we construct the nonrelativistic effective theory, show that the lightest glueball/glueballino states fill a chiral supermultiplet…
We study a class of dark matter models in which the dark matter is a baryon-like composite particle of a confining gauge group and also a pseudo-Nambu-Goldstone boson associated with the breaking of an enhanced chiral symmetry group. The approximate symmetry decouples the dark matter mass from the confinement scale of the new gauge group, leading to correct thermal relic abundances for dark matter masses far below the unitary bound, avoiding the typical conclusion of thermally produced composite dark matter. We explore the available parameter space in a minimal example model based on an SU(2) …
Almost massless mesons created at the condensation scale of extra nonabelian gauge group can be candidates of dark energy source. This can be another motivation for introducing an additional confining force.
We show a constantly accelerated quark as a string solution of the Nambu-Goto action, which is embedded in the bulk background dual to the $\cal{N}$ $=2$ supersymmetric confining Yang-Mills theory. The induced metric of the world sheet for this string solution has an event horizon specified by the fifth coordinate. By an extended Rindler transformation proposed by Xiao, we move to the comoving frame of the accelerated quark-string. Then we find that this horizon is transferred to the event horizon of the bulk and the causal part of the accelerated quark is transformed to a static free-quark in…
This is a review of the recent progress on a holographic description of the Schwinger effect. In 2011, Semenoff and Zarembo proposed a scenario to study the Schwinger effect in the context of the AdS/CFT correspondence. The production rate of quark anti-quark pairs was computed in the Coulomb phase. In particular, it provided the critical value of external electric field, above which particles are freely created and the vacuum decays catastrophically. Then the potential analysis in the holographic approach was invented and it enabled us to study the Schwinger effect in the confining phase as w…
We give necessary criteria for N=1 supersymmetric theories to be in a smoothly confining phase without chiral symmetry breaking and with a dynamically generated superpotential. Using our general arguments we find all such confining SU and Sp theories with a single gauge group and no tree level superpotential.
We study the approach, initiated by Marinari et al., to the static inter-quark potential based on Polyakov lines of finite temporal extent, evaluated in Coulomb gauge. We show that, at small spatial separations, the potential can be understood as being between two separately gauge invariant colour charges. At larger separations Gribov copies obstruct the non-perturbative identification of individually gauge invariant colour states. We demonstrate, for the first time, how gauge invariance can be maintained quite generally by averaging over Gribov copies. This allows us to extend the analysis of…
We introduce a simple scenario where, by starting with a five-dimensional SU(3) gauge theory, we end up with several 4-D parallel branes with localized fermions and gauge fields. Similar to the split fermion scenario, the confinement of fermions is generated by the nontrivial topological solution of a SU(3) scalar field. The 4-D fermions are found to be chiral, and to have interesting properties coming from their 5-D group representation structure. The gauge fields, on the other hand, are localized by loop corrections taking place at the branes produced by the fermions. We show that these two …
The complete absence of isolated quarks reaching particle detectors after high energy collisions suggests that some physical mechanism generates resistance to their propagation in the vacuum. In order to reveal such a mechanism, we analyze the fate of an infinitely heavy quark that is initially propagating in the vacuum with inertial motion. The non-perturbative structure of the vacuum is treated here using the gauge/ gravity correspondence, the isolated quark on the boundary gauge theory is dual to a trailing string moving in the bulk of a higher dimensional curved space. We find that, for a …
Consequences of large $N$ volume independence are examined in conformal and confining gauge theories. In the large $N$ limit, gauge theories compactified on $\R^{d-k} \times (S^1)^k$ are independent of the $S^1$ radii, provided the theory has unbroken center symmetry. In particular, this implies that a large $N$ gauge theory which, on $\R^d$, flows to an IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on $\R^{d-k} \times (S^1)^k$. In other words, finite volume effects are $1/N$ suppressed. In latti…
I begin these three lectures by describing some of the useful things that we have learned about large-N gauge theories using lattice simulations. For example that the theory is confining in that limit, that for many quantities SU(3) is close to SU(oo), and that this includes the strongly coupled gluon plasma just above Tc, thus providing some of the justification needed to make use of gauge-gravity duality in analysing QCD at RHIC/LHC temperatures. I then turn, in a more detailed discussion, to recent progress on the problem of what effective string theory describes confining flux tubes. I des…
We present a lattice study of the phase transitions at zero and nonzero temperature for the $SU(3)$ gauge theory with a varying number of flavours $N_f$ in the fundamental representation of the gauge group. We show that all results are consistent with a lower edge of the conformal window between $N_f=8$ and $N_f=6$. A lower edge in this interval is in remarkable agreement with perturbation theory and recent large-$N$ arguments. .
We study the gravitational dual of a high-energy collision in a confining gauge theory. We consider a linearized approach in which two point particles traveling in an AdS-soliton background suddenly collide to form an object at rest (presumably a black hole for large enough center-of-mass energies). The resulting radiation exhibits the features expected in a theory with a mass gap: late-time power law tails of the form t^(-3/2), the failure of Huygens' principle and distortion of the wave pattern as it propagates. The energy spectrum is exponentially suppressed for frequencies smaller than the…
We revisit the singular IIB supergravity solution describing M fractional 3-branes on the conifold [hep-th/0002159]. Its 5-form flux decreases, which we explain by showing that the relevant \NN=1 SUSY SU(N+M)xSU(N) gauge theory undergoes repeated Seiberg-duality transformations in which N -> N-M. Far in the IR the gauge theory confines; its chiral symmetry breaking removes the singularity of hep-th/0002159 by deforming the conifold. We propose a non-singular pure-supergravity background dual to the field theory on all scales, with small curvature everywhere if the `t Hooft coupling g_s M is la…
Time dependent perturbations of states in the holographic dual of a 3+1 dimensional confining theory are considered. The perturbations are induced by varying the coupling to the theory's most relevant operator. The dual gravitational theory belongs to a class of Einstein-dilaton theories which exhibit a mass gap at zero temperature and a first order deconfining phase transition at finite temperature. The perturbation is realized in various thermal bulk solutions by specifying time dependent boundary conditions on the scalar, and we solve the fully backreacted Einstein-dilaton equations of moti…
For the four-dimensional SU(N) Euclidean Yang-Mills theory in the Landau gauge, we present two sets of gauge field configurations that satisfy the Euclidean equations of motion. These configurations generate four-dimensional chromo-field flux sheets whose spatial cross sections are three-dimensional chromo-field flux tubes. In lattice simulations, they may be detected as center vortices. The first set of gauge field configurations generates chromo-electric flux tubes that should contribute to a chromo-electric flux tube between two static color charges. The string tension for two static color …
We exhibit $N=1$ supersymmetric field theories in confining, Coulomb and Higgs phases. The superpotential and the gauge kinetic terms are holomorphic and can be determined exactly in the various phases. The Coulomb phase generically has points with massless monopoles. When they condense, the theory undergoes a phase transition to a confining phase. When there are points in the Coulomb phase with massless electric charges, their condensation leads to a transition to a Higgs phase. When the Higgs and confinement phases are distinct, we expect to find massless interacting gluons at the transition…
A characteristic signature of quark confinement is the concentration of the chromoelectric field between a static quark-antiquark pair in a flux tube. However, the structure of this flux tube, and hence of the confining force, has not been completely understood. Here we perform new lattice measurements of field distributions on smeared Monte Carlo ensembles in SU(3) gauge theory. On the basis of these simulations we demonstrate that the confining force can be understood using the analogy with the basic principles of electromagnetism as elucidated by Maxwell. We derive a chromomagnetic Lorentz …
In this paper we present a model which can produce boundary confining condition on Dirac field interacting with Abelian or non Abelian gauge fields. The constraint is generated by a scalar field. This kind of model can be the foundation for bag models which can produce confinement. The present work represents among other things a generalization to the non Abelian case of our previous result where the Abelian case was studied. In the $U(1)$ case the coupling to the gauge field contains a term of the form $g(ϕ)j_μ(A^μ +\partial^μB)$ where $B$ is an auxiliary field and $j_μ$ is the Dirac current.…
We review the recent results in the physics of the magnetic monopoles in gluodynamics and a dual formulation of non-Abelian theories, relevant to the physics of the confinement. It occurs that the dual gluon is a U(1) gauge boson, despite of the fact that usual gluons are non-Abelian. The effective infrared Lagrangian for gluodynamics is suggested which leads to the Casimir scaling of the string tension for quarks in various representations. We also show that the results of the calculations in lattice gauge theories confirm our theoretical predictions.
We show that the QCD vacuum (without dynamical quarks) is a dual superconductor at least in the low-energy region in the sense that monopole condensation does really occur. In fact, we derive the dual Ginzburg-Landau theory (i.e., dual Abelian Higgs model) directly from the SU(2) Yang-Mills theory by adopting the maximal Abelian gauge. The dual superconductor can be on the border between type II and type I, excluding the London limit. The masses of the dual Abelian gauge field is expressed by the Yang-Mills gauge coupling constant and the mass of the off-diagonal gluon of the original Yang-Mil…
We compute the inclusive spectrum of produced particles in e+e- annihilation in confining gauge theories that have a gravity dual and show that the momentum distribution exhibits the thermal behavior.
An effective theory based on ensembles of either regular gauge instantons or merons is shown to produce confinement in SU(2) Yang-Mills theory. When the scale is set by the string tension, the action density, topological susceptibility and low-lying glueball spectrum are similar to those arising in lattice QCD. The physical mechanism producing confinement is explained, and a number of analytical insights into the effective theory are presented.
We calculate the string tensions of $k$-strings in SU($N$) gauge theories in both 3 and 4 dimensions. In D=3+1, we find that the ratio of the $k=2$ string tension to the $k = 1$ fundamental string tension is consistent, at the $2 σ$ level, with both the M(-theory)QCD-inspired conjecture and with `Casimir scaling'. In D=2+1 we see a definite deviation from the MQCD formula, as well as a much smaller but still significant deviation from Casimir scaling. We find that in both D=2+1 and D=3+1 the high temperature spatial $k$-string tensions also satisfy approximate Casimir scaling. We point out tha…
