We investigate the dependence of four-dimensional SU(N) gauge theories on the topological theta term at finite temperature and, in particular, across the deconfinement transition. For this purpose, we exploit the lattice formulation of the theory and present numerical results for the expansion of the free energy up to O(theta^6), for N=3 and N=6.
Our numerical analysis shows that the theta dependence of 4D SU(N) gauge theory experiences a drastic change across the deconfinement transition: the low-temperature phase is characterized by a large-N scaling with theta/N as relevant variable, while in the high-temperature phase the scaling variable is just theta and the free energy is essentially determined by the instanton-gas approximation. The crossover between the two different behaviours gets sharper with increasing N, suggesting that the instanton-gas regime sets in just above Tc at large N.
We determine the theta dependence of the deconfinement temperature of SU(3) pure gauge theory, finding that it decreases in presence of a topological theta term. We do that by performing lattice simulations at imaginary theta, then exploiting analytic continuation. We also give an estimate of such dependence in the limit of a large number of colors N, and compare it with our numerical results.
Using the twisted partition function on R^3 x S^1, we argue that the deconfinement phase transition in pure Yang-Mills theory for all simple gauge groups is continuously connected to a quantum phase transition that can be studied in a controlled way. We explicitly consider two classes of theories, gauge theories with a center symmetry, such as SU(N_c) gauge theory for arbitrary N_c, and theories without a center symmetry, such as G_2 gauge theory. The mechanism governing the phase transition is universal and valid for all simple groups. The perturbative one-loop potential as well as monopole-i…
In the holographic model of QCD, theta dependence sharply changes at the point of confinement deconfinement phase transition. In large N QCD such a change in theta behavior can be related to the breakdown of the instanton expansion at some critical temperature T_c. Associating this temperature with confinement-deconfinement phase transition leads to the description of the latter in terms of dissociation of instantons into the fractionally charged instanton quarks. To elucidate this picture, we introduce the nonvanishing chiral condensate in the deconfining phase and assume a specific lagrangia…
We investigate the properties of the deconfinement transition in SU(4) and SU(6) gauge theories. We find that it is a `normal' first order transition in both cases, from which we conclude that the transition is first order in the N->infinity limit. Comparing our preliminary estimates of the continuum values of Tc/sqrt(K) with existing values for SU(2) and SU(3) demonstrates a weak dependence on N for all values of N.
A class of large N SU(N) gauge theories on a compact manifold S^3 X R (with possible inclusion of adjoint matter) is known to show first order deconfinement transition at the deconfinement temperature. This includes the familiar example of pure YM theory and N=4 SYM theory. Here we study the effect of introduction of N_f fundamental matter fields in the phase diagram of the above mentioned gauge theories at small coupling and in the limit of large N and finite N_f/N. We find some interesting features like the termination of the line of first order deconfinement phase transition at a critical p…
We study the phase diagram of non-Abelian pure gauge theories in the presence of a topological theta term. The dependence of the deconfinement temperature on theta is determined on the lattice both by analytic continuation and by reweighting, obtaining consistent results. The general structure of the diagram is discussed on the basis of large-N considerations and of the possible analogies and dualities existing with the phase diagram of QCD in presence of an imaginary baryon chemical potential.
We provide the evidence for the existence of partially deconfined phase in large-$N$ gauge theory. In this phase, the SU($M$) subgroup of SU($N$) gauge group deconfines, where $\frac{M}{N}$ changes continuously from zero (confined phase) to one (deconfined phase). The partially deconfined phase may exist in real QCD with $N=3$.
We demonstrate that weakly coupled, large N, d-dimensional SU(N) gauge theories on a class of compact spatial manifolds (including S^{d-1} \times time) undergo deconfinement phase transitions at temperatures proportional to the inverse length scale of the manifold in question. The low temperature phase has a free energy of order one, and is characterized by a stringy (Hagedorn) growth in its density of states. The high temperature phase has a free energy of order N^2. These phases are separated either by a single first order transition that generically occurs below the Hagedorn temperature or …
We investigate the deconfinement transition of static quarks in SU(N) Yang-Mills theories using a perturbative approach based on a massive extension of the Landau-DeWitt gauge-fixed action, where the gluon mass term is related to the issue of Gribov ambiguities. A leading-order, one-loop calculation of the effective potential for the Polyakov loop produces a deconfinement transition of second order for the SU(2) theory and of first order for SU(3) with transition temperatures in qualitative agreement with known values. We also report on the results of a two-loop calculation of the critical tem…
We report a study of the dependence of 4D SU(N) gauge theories on the topological theta term at finite temperature, and in particular in the large-N limit. We show that the theta dependence drastically changes across the deconfinement transition. The low-temperature phase is characterized by a large-N scaling with theta/N as relevant variable, while in the high-temperature phase the free energy is essentially determined by the dilute instanton-gas approximation, with a simple theta dependence of the free-energy density proportional to 1-Cos(theta).
Some time ago, Svetitsky and Yaffe have argued that -- if the deconfinement phase transition of a (d+1)-dimensional Yang-Mills theory with gauge group G is second order -- it should be in the universality class of a d-dimensional spin model symmetric under the center of G. For d=3 these arguments have been confirmed numerically only in the SU(2) case with center Z(2), simply because all SU(N) Yang-Mills theories with N>=3 seem to have non-universal first order phase transitions. The symplectic groups Sp(N) also have the center Z(2) and provide another extension of SU(2) = Sp(1) to general N. U…
We summarize and extend evidence that the deconfinement phase transition in Yang-Mills theories can be viewed as change of effective non-perturbative degrees of freedom and of symmetries of their interactions. In short, the strings in four dimensions (4d) at temperatures below the critical temperature Tc are replaced by particles, or field theories in 3d at T>Tc. The picture emerges within various approaches based, in particular, on dual models, lattice data and field theoretic models. We concentrate mostly on the lattice data, or on the language of quantum geometry.
We study the relation of confinement and chiral symmetry breaking in gauge theories with non-trivial center, such as SU(N) gauge theories. To this end, we deform these gauge theories by introducing an additional control parameter into the theory and by varying the representation of the quark fields. We then consider a large-d(R) expansion of the effective action, where d(R) denotes the dimension of the representation R of the quark fields. We show how our large-d(R) expansion can be extended in a systematic fashion and discuss the effects of 1/d(R)-corrections on the dynamics close to the fini…
Recently, it has been conjectured that deconfining phase transition in SU(N_c) pure Yang-Mills theories is continuously connected to a quantum phase transition in softly broken N=1 super Yang-Mills on R^{1,2}*S^1. We exploit this conjecture to study the strength of the transition and deconfining temperature as a function of the vacuum angle theta in pure Yang-Mills. We find that the transition temperature is a decreasing function of theta in [0, π), in an excellent agreement with recent lattice simulations. We also predict that the transition becomes stronger for the same range of theta, and c…
The interplay of deconfinement and chiral symmetry restoration are considered in terms of effective theories. We generalize the earlier model studies by considering fermions in higher representations, and study the finite temperature phase diagrams of SU(2) and SU(3) gauge theories with two fermion flavors in fundamental, adjoint or two-index symmetric representations. We discuss our results in relation to recent lattice simulations on these theories and outline possible applications in the context of dynamical electroweak symmetry breaking.
Maximal 't Hooft loops are studied in SO(3) lattice gauge theory at finite temperature T. Tunneling barriers among twist sectors causing loss of ergodicity for local update algorithms are overcome through parallel tempering, enabling us to measure the vortex free energy F and to identify a deconfinement transition at some $β_A^{crit}$. The behavior of F below $β_A^{crit}$ shows however striking differences with what is expected from discretizations in the fundamental representation.
We consider a simple massive extension of the Landau-DeWitt gauge for SU($N$) Yang-Mills theory. We compute the corresponding one-loop effective potential for a temporal background gluon field at finite temperature. At this order the background field is simply related to the Polyakov loop, the order parameter of the deconfinement transition. Our perturbative calculation correctly describes a quark confining phase at low temperature and a phase transition of second order for $N=2$ and weakly first order for $N=3$. Our estimates for the transition temperatures are in qualitative agreement with v…
Effects of the theta parameter are studied in Witten's model of holographic 4d Yang-Mills, where theta is the coefficient of the CP-breaking topological term. First, the gravity background, including the full backreaction of the RR form dual to the theta parameter, is revisited. Then, a number of observables are computed holographically: the ground-state energy density, the string tension, the 't Hooft loop, the light scalar glueball mass, the baryon mass scale, the critical temperature for deconfinement - and thus the whole (T, theta) phase diagram - and the entanglement entropy. A simple rul…
We study the phase structure of N=1 supersymmetric Yang-Mills theory on R^3XS^1, with massive gauginos, periodic around the S^1, with Sp(2N) (N>=2), Spin(N) (N>=5), G_2, F_4, E_6, E_7, E_8 gauge groups. As the gaugino mass m is increased, with S^1 size and strong coupling scale fixed, we find a first-order phase transition both for theories with and without a center. This semiclassically calculable transition is driven, as in SU(N) and G_2, arxiv.org/abs/1205.0290 and arxiv.org/abs/1212.1238, by a competition between monopole-instantons and exotic topological "molecules"---"neutral" or "magnet…
We propose a novel approach to the confinement-deconfinement transition in Yang-Mills theories in the context of gauge-fixed calculations. The method is based on a background-field generalisation of the Landau gauge (to which it reduces at vanishing temperature) with a given, center-symmetric background. This is to be contrasted with most implementations of background field methods in gauge theories, where one uses a variable, self-consistent background. Our proposal is a bona fide gauge fixing that can easily be implemented on the lattice and in continuum approaches. The resulting gauge-fixed…
We study $SU(N_c)$ gauge theories with Dirac fermions in representations ${\cal{R}}$ of nonzero $N$-ality, coupled to axions. These theories have an exact discrete chiral symmetry, which has a mixed 't Hooft anomaly with general baryon-color-flavor backgrounds, called the "BCF anomaly" in arXiv:1909.09027. The infrared theory also has an emergent $\mathbb Z_{N_c}^{(1)}$ $1$-form center symmetry. We show that the BCF anomaly is matched in the infrared by axion domain walls. We argue that $\mathbb Z_{N_c}^{(1)}$ is spontaneously broken on axion domain walls, so that nonzero $N$-ality Wilson loop…
A new method is proposed for determining the critical indices of the deconfinement transition in gauge theories, based on the finite-size scaling analysis of simple lattice operators, such as the plaquette. A precise determination of the critical index $ν$, in agreement with the prediction of the Svetitsky-Yaffe conjecture, is obtained for SU(3) gauge theory in (2+1)-dimension. Preliminary results for SU(2) in (3+1)-dimension are also given.
We introduce a new method for determining the critical indices of the deconfinement transition in gauge theories. The method is based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We test the method for the case of SU(3) pure gauge theory in (2+1) dimensions and obtain a precise determination of the critical index $ν$, in agreement with the prediction of the Svetitsky-Yaffe conjecture.
We study the theta dependence of the spectrum of four-dimensional SU(N) gauge theories, where theta is the coefficient of the topological term in the Lagrangian, for N>=3 and in the large-N limit. We compute the O(theta^2) terms of the expansions around theta=0 of the string tension and the lowest glueball mass, respectively sigma(theta) = sigma (1 + s_2 theta^2 + ...) and M(theta) = M (1 + g_2 theta^2 + ...), where sigma and M are the values at theta=0. For this purpose we use numerical simulations of the Wilson lattice formulation of SU(N) gauge theories for N=3,4,6. The O(theta^2) coefficie…
We study the theta dependence of the spectrum of four-dimensional SU(N) gauge theories, where theta is the coefficient of the topological term in the Lagrangian, for N>=3 and in the large-N limit. We compute the O(theta^2) terms of the expansions around theta=0 of the string tension and the lowest glueball mass, respectively sigma(theta) = sigma (1 + s_2 theta^2 + ...) and M(theta) = M (1 + g_2 theta^2 + ...), where sigma and M are the values at theta=0. For this purpose we use numerical simulations of the Wilson lattice formulation of SU(N) gauge theories for N=3,4,6. The O(theta^2) coefficie…
Pure Yang-Mills theory has a finite-temperature phase transition, separating the confined and deconfined bulk phases. Svetitsky and Yaffe conjectured that if this phase transition is of second order, it belongs to the universality class of transitions for particular scalar field theories in one lower dimension. We examine Yang-Mills theory with the symplectic gauge groups Sp(N). We find new evidence supporting the Svetitsky-Yaffe conjecture and make our own conjecture as to which gauge theories have a universal second order deconfinement phase transition.
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.
We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature using a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and of the related background field effective potential for the SU(2) theory to any compact and connex Lie group with a simple Lie algebra. We discuss in detail the SU(3) theory, where the two-loop corrections yield improved values for the first-order transition temperature as compared to the one-loop result. We also show that c…
We study the dependence of the free energy on the CP violating angle theta, in four-dimensional SU(N) gauge theories with N >= 3, and in the large-N limit. Using the Wilson lattice formulation for numerical simulations, we compute the first few terms of the expansion of the ground-state energy F(theta) around theta = 0, F(theta) - F(0) = A_2 theta^2 (1 + b_2 theta^2 + ...). Our results support Witten's conjecture: F(theta) - F(0) = A theta^2 + O(1/N) for theta < pi. We verify that the topological susceptibility has a nonzero large-N limit chi_infinity = 2A with corrections of O(1/N^2), in subs…
We present recent results on the theta-dependence of four-dimensional SU(N) gauge theories, where theta is the coefficient of the CP-violating topological term in the Lagrangian. In particular, we study the scaling behavior of these theories, by Monte Carlo simulations at imaginary theta. The numerical results provide good evidence of scaling in the continuum limit. The imaginary theta dependence of the ground-state energy turns out to be well described by the first few terms of related expansions around theta=0, providing accurate estimates of the first few coefficients, up to O(theta^6).
We review results concerning the theta dependence of 4D SU(N) gauge theories and QCD, where theta is the coefficient of the CP-violating topological term in the Lagrangian. In particular, we discuss theta dependence in the large-N limit. Most results have been obtained within the lattice formulation of the theory via numerical simulations, which allow to investigate the theta dependence of the ground-state energy and the spectrum around theta=0 by determining the moments of the topological charge distribution, and their correlations with other observables. We discuss the various methods which …
The deconfinement transition in SU($N_c$) Yang--Mills is investigated by Monte Carlo simulations of the gauge theory discretized on a spacetime lattice. We present new results for $ 4 \le N_c \le 8$ (in particular, for $N_c = 5$ and $N_c = 7$), which are analysed together with previously published results. The increased amount of data, the improved statistics and simulations closer to the continuum limit provide us with better control over systematic errors. After performing the thermodynamic limit, numerical results for the ratio of the critical temperature $T_c$ over the square root of the s…
It is shown that permanent confinement in three-dimensional compact U(1) gauge theory can be destroyed by matter fields in a deconfinement transition. This is a consequence of a non-trivial infrared fixed point caused by matter, and an anomalous scaling dimension of the gauge field. This leads to a logarithmic interaction between the defects of the gauge-fields, which form a gas of magnetic monopoles. In the presence of logarithmic interactions, the original electric charges are unconfined. The confined phase which is permanent in the absence of matter fields is reached at a critical electric …
The phase structure of hot gauge theories with dynamical matter fields is reexamined in the canonical ensemble with respect to triality. We discuss properties of chromoelectric and chromomagnetic sectors of the theory and show whereas electric charges carrying a unit of Z(N) charge are screened at high temperatures via dynamical matter loops, this is not the case for the Z(N) magnetic flux. An order parameter is constructed to probe the realization of local Z(N) symmetry in the magnetic sector. We argue this order parameter may be used to detect the deconfinement phase transition which is defi…
We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2)and SU(2)/Z_2 gauge theories, compactified on a small spatial circle R^(1,2) x S^1, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R^2 x T^2. Similarly, thermal gauge theories of higher rank are dual to new families of "affine" XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made …
Under very general assumptions we show that Vafa-Witten theorem on vector symmetries in vector-like theories can be extended to some physically relevant gauge theories with non-positive definite integration measure as QCD with a theta-vacuum term.
We study the deconfinement phase transition in $ (2+1) $-dimensional holographic $ SU(N) $ gauge theories in the presence of an external magnetic field from the holographic hard and soft wall models. We obtain exact solutions for the critical temperature of the deconfinement transition for any range of magnetic field. As a consequence, we find a critical magnetic field $(B_c)$, in which the critical temperature $(T_c)$ vanishes; for $B<B_c$ we have an inverse magnetic catalysis and for $ B>B_c $ we have a magnetic catalysis.
We compare vacuum dynamics of abelian versus non abelian lattice gauge theories in presence of external fields. We find that the deconfinement temperature of non abelian theories depends on the strength of a constant abelian chromomagnetic field end eventually goes to zero. On the contrary such an effect is not shared by abelian theories. We argue on the relevance of this result to understand the QCD vacuum.
In the weak coupling limit of ${\rm SU}(N)$ Yang-Mills theory and the ${\rm O}(N)$ vector model, explicit state counting allows us to demonstrate the existence of a partially deconfined phase: $M$ of $N$ colors deconfine, and $\frac{M}{N}$ gradually grows from zero (confinement) to one (complete deconfinement). We point out that the mechanism admits a simple interpretation in the form of spontaneous breaking of gauge symmetry. In terms of the dual gravity theory, such breaking occurs during the formation of a black hole. We speculate whether the breaking and restoration of gauge symmetry can s…
We investigate the effects of dissipation in the deconfinement transition for pure SU(2) and SU(3) gauge theories. Using an effective theory for the order parameter, we study its Langevin evolution numerically. Noise effects are included for the case of SU(2). We find that both dissipation and noise have dramatic effects on the spinodal decomposition of the order parameter and delay considerably its thermalization. For SU(3) the effects of dissipation are even larger than for SU(2).
Effective three-dimensional Polyakov loop theories derived from QCD by strong coupling and hopping expansions are valid for heavy quarks and can also be applied to finite chemical potential $μ$, due to their considerably milder sign problem. We apply the Monte-Carlo method to the $N_f=1,2$ effective theories up to $\mathcal{O}(κ^4)$ in the hopping parameter at $μ=0$ to determine the critical quark mass, at which the first-order deconfinement phase transition terminates. The critical end point obtained from the effective theory to order $\mathcal{O}(κ^2)$ agrees well with 4-dimensional QCD simu…
A toy model is proposed for four dimensional non-abelian gauge theories coupled to a large number of fermionic degrees of freedom. As the number of flavors is varied the gauge theory may be confining, walking or conformal. The toy model mimicking this feature is the two dimensional O(3) sigma model with a theta-term. For all theta the model is asymptotically free. For small theta the model is confining in the infra red, for theta = pi the model has a non-trivial infra red fixed point and consequently for theta slightly below pi the coupling walks. The first step in investigating the notoriousl…
Computing the entanglement entropy in confining gauge theories is often accompanied by puzzles and ambiguities. In this work we show that compactifying the theory on a small circle $\mathbb S^1_L$ evades these difficulties. In particular, we study Yang-Mills theory on $\mathbb R^3\times \mathbb S^1_L$ with double-trace deformations or adjoint fermions and hold it at temperatures near the deconfinement transition. This theory is dual to a multi-component (electric-magnetic) Coulomb gas that can be mapped either to an XY-spin model with $\mathbb Z_p$-preserving perturbations or dual Sine-Gordon …
We present numerical results for the deconfinement phase transition in Sp(2) and Sp(3) Yang-Mills theories in (2+1)-D and (3+1)-D. We then make a conjecture on the order of this phase transition in Yang-Mills theories with general Lie groups G = SU(N), SO(N), Sp(N) and with exceptional groups G = G(2), F(4), E(6), E(7), E(8).
We review some analytic results on the deconfinement transition in pure lattice gauge theories. In particular we discuss the relationship between the deconfinement transition in the $(d+1)$-dimensional $SU(2)$ model and the magnetization transition in the $d$-dimensional Ising model. This analysis leads to a precise estimate of the deconfinement temperature which agrees well with that obtained with a Montecarlo simulation in the case in which the lattice has only one link in the compactified time direction.
In this contribution we review some recent results about the emergence of 2D integrable systems in 3D Lattice Gauge Theories near the deconfinement transition. We focus on some concrete examples involving the flux tube thickness, the ratio of k-string tensions and Polyakov loops correlators in various models.
We study two-dimensional U($N$) and SU($N$) gauge theories with a topological term on arbitrary surfaces. Starting from a lattice formulation we derive the continuum limit of the action which turns out to be a generalisation of the heat kernel in the presence of a topological term. In the continuum limit we can reconstruct the topological information encoded in the theta term. In the topologically trivial cases the theta term gives only a trivial shift to the ground state energy but in the topologically nontrivial ones it remains to be coupled to the dynamics in the continuum. In particular fo…
U(1) lattice gauge theory with $θ$-term is investigated by real space renormalization group approach. Flows of renormalized coupling constants are analyzed. For each $θ$, renormalization flows converge to a single trajectory irrespective of bare coupling constants of real action. For $θ\not= π$ the system is in the confinement phase controlled by an infrared fixed point. We found a phase transition at $θ= π$. Imaginary part of the action given by $θ$-term stays fixed under renormalization group transformations leading to deconfinement.
In a recent work we have proposed a perturbative approach for the study of the phase transition of pure Yang-Mills theories at finite temperature. This is based on a simple massive extension of background field methods in the Landau-DeWitt gauge, where the gluon mass term is related to the existence of Gribov ambiguities. We have shown that a one-loop calculation of the background field effective potential describes well the phase structure of the SU(2) and SU(3) theories. Here, we present the calculation of the next-to-leading-order contribution in perturbation theory for the SU(2) case. In p…
We investigate the connection between Color Confinement and thermal Abelian monopoles populating the deconfined phase of SU(2) Yang-Mills theory, by studying how the statistical properties of the monopole ensemble change as the confinement/deconfinement temperature is approached from above. In particular we study the distribution of monopole currents with multiple wrappings in the Euclidean time direction, corresponding to two or more particle permutations, and show that multiple wrappings increase as the deconfinement temperature is approached from above, in a way compatible with a condensati…
The phase structure of hot gauge theories with dynamical matter fields is reexamined in the canonical ensemble with respect to triality. Since this ensemble implies a projection to the zero triality sector of the theory we introduce a proper quantity which is able to reveal a critical behaviour of the theory with fundamental quarks. We discuss the properties of both the chromoelectric and chromomagnetic sectors of the theory and show while electric charges carrying a unit of Z(N) charge are screened at high temperatures by dynamical matter loops, this is not the case for the Z(N) magnetic flux…
We review recent results on the theta dependence of the ground-state energy and spectrum of four-dimensional SU(N) gauge theories, where theta is the coefficient of the CP-violating topological term F-Fdual in the Lagrangian. In particular, we discuss the results obtained by Monte Carlo simulations of the lattice formulation of QCD, which allow the investigation of theta dependence around theta=0 by determining the moments of the topological charge distribution, and their correlations with other observables. The results for N=3 and larger values of N support the scenario obtained by general la…
We study constraints on thermal phase transitions of ${\rm SU}(N_c)$ gauge theories by using the 't Hooft anomaly involving the center symmetry and chiral symmetry. We consider two cases of massless fermions: (i) adjoint fermions, and (ii) $N_f$ flavors of fundamental fermions with a nontrivial greatest common divisor ${\rm gcd}(N_c,N_f) \neq 1$. For the first case (i), we show that the chiral symmetry restoration in terms of the standard Landau-Ginzburg effective action is impossible at a temperature lower than that of deconfinement. For the second case (ii), we introduce a modified version o…
We discuss the phase structure of N D4 branes wrapped on a temporal (Euclidean) and a spatial circle, in terms of the near-horizon AdS geometries. This system has been studied previously to understand four dimensional pure SU(N) Yang-Mills theory (YM4) through holography. In the usual treatment of the subject, the phase transition between the AdS soliton and the black D4 brane is interpreted as the strong coupling continuation of the confinement/deconfinement transition in YM4. We show that this interpretation is not valid, since the black D4 brane and the deconfinement phase of YM4 have diffe…
Center for Theoretical Physics, Massachusetts Institute of Technology（麻省理工学院理论物理中心）；Argonne National Laboratory（阿贡国家实验室）；Pacific Quantum Center, Far Eastern Federal University（远东联邦大学太平洋量子中心）；Institut Denis Poisson CNRS/UMR 7013, Université de Tours（图尔大学丹尼斯·泊松研究所（法国国家科学研究中心/联合研究单位7013））
We study the machine learning techniques applied to the lattice gauge theory's critical behavior, particularly to the confinement/deconfinement phase transition in the SU(2) and SU(3) gauge theories. We find that the neural network, trained on lattice configurations of gauge fields at an unphysical value of the lattice parameters as an input, builds up a gauge-invariant function, and finds correlations with the target observable that is valid in the physical region of the parameter space. In particular, if the algorithm aimed to predict the Polyakov loop as the deconfining order parameter, it …
Conformal perturbation theory is a powerful tool to describe the behavior of statistical-mechanics models and quantum field theories in the vicinity of a critical point. In the past few years, it has been extensively used to describe two-dimensional models and recently has also been extended to three-dimensional models. We show here that it can also be used to describe the behavior of four-dimensional lattice gauge theories in the vicinity of a critical point. As an example, we discuss the two-point correlator of Polyakov loops close to the thermal deconfinement transition of $SU(2)$ Yang-Mill…
Effective Lagrangians for Quantum Chromodynamics (QCD) especially suited for understanding deconfinement and chiral symmetry restoration at nonzero temperature and matter density are reviewed. These effective theories allow one to study generic properties of phase transitions using non-order parameter fields without loosing the information encoded in the true order parameter. {}For the pure gauge theory we demonstrate that, near the deconfining phase transition, the center group symmetry is naturally linked to the conformal anomaly. Another relevant outcome is that when the theory contains als…
