We consider four dimensional $\mathcal{N}=1$ gauge theories that are S-confining, that is they are dual to a Wess-Zumino model. S-confining theories with a simple gauge group have been classified. We prove all the S-confining dualities in the list, when the matter fields transform in rank-$1$ and/or rank-$2$ representations. Our only assumptions are the S-confining dualities for $SU(N)$ with $N+1$ flavors and for $Usp(2N)$ with $2N+4$ fundamentals. The strategy consists in a sequence of deconfinements and re-confinements. We pay special attention to the explicit superpotential at each step.
We construct a three dimensional deconfinement method which enables us to find new three-dimensional dualities and we apply various techniques developed in four dimensional supersymmetric gauge theories, such as the product gauge groups and Seiberg-Witten curves to the three dimensional $\mathcal{N}=2$ supersymmetric gauge theories. Dual descriptions of three dimensional $\mathcal{N}=2$ supersymmetric gauge theories which involve two-index matters, for example, adjoint, symmetric, and anti-symmetric matters without superpotentials can be obtained. These matters are described in terms of s-conf…
It is an interesting question whether a given infra-red duality between quantum field theories can be explained in terms of other more elementary dualities. For example recently it has been shown that mirror dualities can be obtained by iterative applications of Seiberg-like dualities. In this paper we continue this line of investigation focusing on theories with tensor matter. In such cases one can apply the idea of deconfinement, which consists of trading the tensor matter for extra gauge nodes by means of a suitable elementary duality. This gives an auxiliary dual frame which can then be ma…
We apply the technique of sequential deconfinement to the four dimensional $\mathcal{N}\!=\!1$ $Usp(2N)$ gauge theory with an antisymmetric field and $2F$ fundamentals. The fully deconfined frame is a length-$N$ quiver. We use this deconfined frame to prove the known self-duality of $Usp(2N)$ with an antisymmetric field and $8$ fundamentals. Along the way we encounter a subtlety: in certain quivers with degenerate holomorphic operators, a naive application of Seiberg duality rules leads to an incorrect superpotential or chiral ring. We also consider the reduction to $3d$ $\mathcal{N}\!=\!2$ th…
We describe a monopole-like order parameter for the confinement-deconfinement transition in gauge theories where dynamical charges and monopoles coexist. It has been recently proposed in a collaboration with J. Froehlich. It avoids an inconsistency in the treatment of small scales present in earlier definitions of monopole fields by respecting Dirac's quantization condition for electromagnetic fluxes. An application to SU(2) lattice Yang-Mills theory is outlined, naturally fitting in the 't Hooft scenario for confinement.
We study analytical solutions of charged black holes and thermally charged AdS with generalized warped factors in Einstein-Maxwell-Dilaton system. We calculate Euclidean action for charged AdS and thermally charged AdS. The actions in both backgrounds are regularized by the method of background subtraction. The study of phase transition between charged black hole and thermally charged AdS gives an insight to the confinement/deconfinement transition. The plots of grand potential vs temperature and chemical potential vs transition temperature are obtained.
We argue that, at finite temperature, parity invariant non-compact electrodynamics with massive electrons in 2+1 dimensions can exist in both confined and deconfined phases. We show that an order parameter for the confinement-deconfinement phase transition is the Polyakov loop operator whose average measures the free energy of a test charge that is not an integral multiple of the electron charge. The effective field theory for the Polyakov loop operator is a 2-dimensional Euclidean scalar field theory with a global discrete symmetry $Z$, the additive group of the integers. We argue that the re…
We study the T-μ phase diagram of anisotropic media, created in heavy-ion collisions (HIC). Such a statement of the problem is due to several indications that this media is anisotropic just after HIC. To study T-μ phase diagram we use holographic methods. To take into account the anisotropy we use an anisotropic black brane solutions for a bottom-up QCD approach in 5-dim Einstein-dilaton-two-Maxwell model constructed in our previous work. We calculate the minimal surfaces of the corresponding probing open string world-sheet in anisotropic backgrounds with various temperatures and chemical pote…
We study the thermodynamics of the hard wall model, which consists in the introduction of an infrared cut-off in asymptotically AdS spaces. This is a toy model for confining backgrounds in the context of the gauge/gravity correspondence. We use holographic renormalization and reproduce the existence of a Hawking Page phase transition recently discussed by Herzog. We also show that the entropy jumps from $N^0$ to $N^2$, which reinforces the interpretation of this transition as the gravity dual of confinement/deconfinement. We also show that similar results hold for the phenomenologically motiva…
The 1+1 dimensional bosonised Schwinger model with a generalized gauge invariant regularisation has been studied in a noncommutative scenario to investigate the fate of the transition from confinement to deconfinement observed in the commutative setting. We show that though the fuzziness of space time introduces new features in the confinement scenario, it does not affect the deconfining limit.
Non-central heavy ion collisions lead to the production of a quark gluon plasma with angular momentum. We investigate, using holographic AdS/QCD models, how does rotation of the medium affects the confinement/deconfinement transition temperature $T_c$. In holographic models, this transition is represented by a Hawking-Page process involving two asymptotically anti-de Sitter spaces. The plasma is represented here by extending the holographic approach to anti-de Sitter spaces with cylindrical symmetry. Then, the rotation of the medium is introduced through a Lorentz boost. We consider hard and s…
Under a Scherk-Schwarz compactification, the AdS soliton and black brane provide a dual description to a confinement/deconfinement phase transition. We extend this construction to asymptotically Lifshitz spacetimes. In particular, we show that there must be a phase transition between the soliton and black hole if the solutions exist. We also construct these solutions numerically and compute the phase diagram.
We give a new criterion of quark confinement/deconfinement by deriving a low-energy effective theory of QCD. The effective theory can explain Abelian dominance in low-energy physics of QCD, especially, quark confinement. Finally, we apply the above criterion to the large flavor QCD and discuss its phase structure. The result suggests the existence of conformal phase.
In hep-th/0402219 we considered large N zero-coupling d-dimensional U(N) gauge theories, with N_f matter fields in the fundamental representation on a compact spatial manifold S^{d-1}x time, with N_f/N finite. This class of theories undergo a 3rd order deconfinement transition. As a consequence it was proposed that the dual string theory has a 3rd order phase-transition to a black hole at high temperature. In this paper we argue that the same conclusions are valid for such theories at any finite order in perturbation theory in the 't Hooft coupling lambda and N_f/N. It is conjectured that this…
We consider, from several complementary perspectives, the physics of confinement and deconfinement in the 2+1 dimensional Georgi-Glashow model. Polyakov's monopole plasma and 't Hooft's vortex condensation are discussed first. We then discuss the physics of confining strings at zero temperature. We review the Hamiltonian variational approach and show how the linear confining potential arises in this framework. The second part of this review is devoted to study of the deconfining phase transition. We show that the mechanism of the transition is the restoration of 't Hooft's magnetic symmetry in…
We study low-energy dynamics of three-dimensional $\mathcal{N}=2$ $SU(N)$ "chiral" gauge theories with $F$ fundamental and $\bar{F}$ anti-fundamental matters without a Chern-Simons term. Compared to a naive semi-classical analysis of the Coulomb branch, its quantum structure is highly richer than expected due to so-called "dressed" Coulomb branch (monopole) operators. We propose dualities and confinement phases for the "chiral" $SU(N)$ theories. The theories with $N>F > \bar{F}$ exhibit spontaneous supersymmetry breaking. The very many Coulomb branch operators generally remain exactly massless…
Cavitation is a process where the viscous terms in a relativistic fluid result in reducing the effective pressure, thus facilitating the nucleation of bubbles of a stable phase. The effect is particularly pronounced in the vicinity of a (weak) first-order phase transition. We use the holographic correspondence to study cavitation in a strongly coupled planar cascading gauge theory plasma close to the confinement/deconfinement phase transition. While in this particular model the shift of the deconfinement temperature due to cavitation does not exceed 5%, we speculate that cavitation might be im…
We study the subregion complexity in a semi-analytical holographic QCD model. Two cases with different warped factor are considered and both can realize confinement-deconfinement transition. By studying the behavior of the renormalized holographic complexity density $\hat{\cal C}$ versus the subregion length scale $\ell$, we find that for both cases, $\hat{\cal C}$ always experiences a discontinuity at certain critical value $\ell_c$ in confinement phases, while it is always continuous in deconfinement phases. This property may be seen as a signal to characterize confinement or deconfinement p…
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 study confinement-deconfinement phase transition for heavy quarks in a bottom-up holographic QCD model. We consider a black hole background in an Einstein-Maxwell-scalar system and add probe open strings to the background. Combining the various configurations of the open strings and the phase structure of the black hole background itself, we obtain the confinement-deconfinement phase diagram for heavy quarks in the holographic QCD model.
We briefly outline several main results concerning various new physically relevant features found in gravity -- both ordinary Einstein or $f(R)=R+R^2$ gravity in the first-order formalism, coupled to a special kind of nonlinear electrodynamics containing a square-root of the standard Maxwell Lagrangian and known to produce charge confinement in flat spacetime.
We propose a new quantity which describes the confinement-deconfinement transition based on topological properties of QCD. The quantity which we call the quark number holonomy is defined as the integral of the quark number susceptibility along the closed loop of $θ$ where $θ$ is the dimensionless imaginary chemical potential. Expected behavior of the quark number holonomy at finite temperature is discussed and its asymptotic behaviors are shown.
The problem of the phase transition of a Z(3) spin system is a complex issue. A numerical simulation in the framework of the mean field theory using the Metropolis algorithm reveals: (a) the existence of second order phase transition with a degenerated critical point which could be considered as a state of resonance (b) hysteresis phenomena which are accompanied with tricritical crossover around the end point of first order transition. Based on these results we propose a scenario about confinement-deconfinement phase transition in SU(3) symmetry of color QCD which, as it is known, has the same…
We study 3d $\mathcal{N}=2$ SQCD with symplectic and orthogonal gauge groups and adjoint matter. For $USp(2n)$ with two fundamentals and $SO(N)$ with one vector these models have been recently shown to s-confine. Here we corroborate the validity of this proposal by relating it to the confinement of $USp(2n)$ with four fundamentals and an antisymmetric tensor, using exact mathematical results coming from the analysis of the partition function on the squashed three-sphere. Our analysis allows us to conjecture new s-confining theories for a higher number of fundamentals and vectors, in presence o…
We study the gravity dual of four dimensional pure Yang-Mills theory through D4 branes, as proposed by Witten (holographic QCD). In this holographic QCD, it has been widely believed that the confinement phase in the pure Yang-Mills theory corresponds to the AdS D4 soliton in gravity and the deconfinement phase corresponds to the black D4 brane. We inspect this conjecture carefully and show that the correspondence between the black D4 brane and the deconfinement phase is not correct. Instead, by using a slightly different set up, we find an alternative gravity solution called "localized soliton…
Band-inverted electron-hole bilayers support quantum spin Hall insulator and exciton condensate phases. We investigate such a bilayer in an external magnetic field. We show that the interlayer correlations lead to formation of a helical quantum Hall exciton condensate state. In contrast to the chiral edge states of the quantum Hall exciton condensate in electron-electron bilayers, existence of the counterpropagating edge modes results in formation of a ground state spin-texture not supporting gapless single-particle excitations. This feature has deep consequences for the low energy behavior of…
We investigate the confinement-deconfinement transition at finite temperature in terms of the probability distribution of Polyakov-loop complex-phase via the Jensen-Shannon divergence. The Jensen-Shannon divergence quantifies the difference of two probability distributions, namely the target and reference probability distributions. We adopt the complex-phase distributions of the spatially averaged Polyakov loop at $μ/T=0$ and $μ/T=iπ/3$ as the target and reference distributions, respectively. It is shown that the Jensen-Shannon divergence has the inflection point when the target system approac…
We conjecture that the confinement- deconfinement phase transition in QCD at large number of colors N and N_f\ll N at T\neq 0 and μ\neq 0 is triggered by the drastic change in θbehavior. The conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at the value of temperature T=T_c where θdependence experiences a sudden change in behavior[1]. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the θdependence) are under complete theoretical control for T>T_c, s…
We present new anisotropic black brane solutions in 5D Einstein-dilaton-two-Maxwell system. The anisotropic background is specified by an arbitrary dynamical exponent $ν$, a nontrivial warp factor, a non-zero dilaton field, a non-zero time component of the first Maxwell field and a non-zero longitudinal magnetic component of the second Maxwell field. The blackening function supports the Van der Waals-like phase transition between small and large black holes for a suitable first Maxwell field charge. The isotropic case corresponding to $ν= 1$ and zero magnetic field reproduces previously known …
We discuss in some detail the properties of gravity (including f(R)-gravity) coupled to non-standard nonlinear gauge field system containing a square root of the usual Maxwell Lagrangian. The latter is known to produce in flat spacetime a QCD-like confinement. Inclusion of gravity triggers various physically interesting effects: new mechanism for dynamical generation of cosmological constant; non-standard black hole solutions with constant vacuum electric field and with "hedge-hog"-type spacetime asymptotics, which are shown to obey the first law of black hole thermodynamics; new "tubelike" so…
We give another derivation of quark confinement in QCD from the viewpoint of the low-energy effective Abelian gauge theory of QCD obtained via Abelian projection. It is based on the recently discovered Berezinskii-Kosterlitz-Thouless phase transition in the four-dimensional Abelian gauge theory. Moreover, we show that there exists a critical gauge coupling constant in QCD, above which confinement set in and below which there is no confinement. In a SU(N) gauge theory with $N_f$ flavored fermions, we argue that this leads to a critical value of fermion flavors $N_f^c$ for the confinement as wel…
In a spontaneously dimerized quantum antiferromagnet, spin-1/2 excitations (spinons) are confined in pairs by strings akin to those confining quarks in non-abelian gauge theories. The system has multiple degenerate ground states (vacua) and domain walls between regions of different vacua. For two vacua, we demonstrate that spinons on a domain wall are liberated, in a mechanism strikingly similar to domain-wall deconfinement of quarks in variants of quantum chromodynamics. This observation not only establishes a novel phenomenon in quantum magnetism, but also provides a new direct link between …
In this paper we consider the influence of relativistic rotation on the confinement/deconfinement transition in gluodynamics within lattice simulation. We perform the simulation in the reference frame which rotates with the system under investigation, where rotation is reduced to external gravitational field. To study the confinement/deconfinement transition the Polyakov loop and its susceptibility are calculated for various lattice parameters and the values of angular velocities which are characteristic for heavy-ion collision experiments. Different types of boundary conditions (open, periodi…
In the holographic AdS/QCD approach, the confinement/deconfinement transition is associated with the Hawking-Page transition of a thermal anti-de Sitter (AdS) space to an AdS black hole. In the case of the hard wall model, the thermal transition takes place in the planar AdS thanks to the introduction of an infrared cut-off in the geometry. The corresponding thermodynamic entropy of the $SU(N) $ gauge theory jumps from proportional to $N^0$ in the confined hadronic phase to proportional to $N^2$ in the plasma phase, corresponding to the presence of the color degrees of freedom. The Hawking-Pag…
We present numerical evidence for a transition between the Klebanov-Strassler background and a solution describing a black hole in the class of cascading solutions in the chirally restored phase. We also present a number of properties of this solution, including the running of the coupling constant, the viscosity to entropy ratio and the drag force on a quark moving in this background.
We study the confinement/deconfinement transition in the D0-brane matrix model (often called the BFSS matrix model) and its one-parameter deformation (the BMN matrix model) numerically by lattice Monte Carlo simulations. Our results confirm general expectations from the dual string/M-theory picture for strong coupling. In particular, we observe the confined phase in the BFSS matrix model, which is a nontrivial consequence of the M-theory picture. We suggest that these models provide us with an ideal framework to study the Schwarzschild black hole, M-theory, and furthermore, the parameter regio…
We consider large N zero-coupling d-dimensional U(N) gauge theories, with N_f matter fields in the fundamental representation on a compact spatial manifold S^{d-1} x time, with N_f/N finite. The Gauss' law constraint induces interactions among the fields, in spite of the zero-coupling. This class of theories undergo a 3rd order deconfinement phase transition at a temperature T_c proportional to the inverse length scale of the compact manifold. The low-temperature phase has a free-energy of {\cal O} (N^2_f), interpreted as that of a gas of (color singlet) mesons and glueballs. The high-temperat…
A family of deformed black branes is employed to examine the confinement/deconfinement phase transition in AdS/QCD. The holographic entanglement entropy (HEE) plays the role of the order parameter driving the confinement/deconfinement phase transition. The binding energy of quark-antiquark bound states and the critical length that makes a null variation of the HEE, together with the critical temperature separating the deconfined quark-gluon plasma to the confined hadronic phase, are discussed in the deformed black brane background, matching current experimental hadronic data.
The one-dimensional lattice Schwinger model has recently been realized by using bosons in optical lattices. This model contains both confinement and deconfinement phases, whose phase diagram is controlled by the mass of the matter field and the topological angle. Since varying the mass of matter field is straightforward experimentally, we propose how to tune the topological angle, allowing accessing the entire phase diagram. We propose that direct experimental evidence of confinement and deconfinement can be obtained by measuring whether a physical charge is localized around a fixed gauge char…
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…
We give an analytical derivation of the confinement/deconfinement phase transition at finite temperature in the $SU(N)$ Yang-Mills theory in the $D$-dimensional space time for $D>2$. For this purpose, we use a novel reformulation of the Yang-Mills theory which allows the gauge-invariant gluonic mass term, and calculate analytically the effective potential of the Polyakov loop average concretely for the $SU(2)$ and $SU(3)$ Yang-Mills theories by including the gauge-invariant dynamical gluonic mass $M$. For $D=4$, we give an estimate on the transition temperature $T_d$ as the ratio $T_d/M$ to th…
We present arguments suggesting that large size overlapping instantons are the driving mechanism of the confinement-deconfinement phase transition at nonzero chemical potential mu. The arguments are based on the picture that instantons at very large chemical potential in the weak coupling regime are localized configurations with finite size rho~1/mu. At the same time, the same instantons at smaller chemical potential in the strong coupling regime are well represented by the so-called instanton-quarks with fractional topological charge 1/Nc. We estimate the critical chemical potential mu_c(T) w…
A model for the infrared sector of Yang-Mills theory based on magnetic vortices represented by (closed) random surfaces is investigated using lattice Monte Carlo methods. The random surfaces are governed by a surface area action and a curvature action. The model generates a finite-temperature deconfinement transition; the coupling constants of the model can be chosen such as to reproduce the SU(2) Yang-Mills ratio of the deconfinement temperature to the square root of the zero-temperature string tension, T_c / sqrt{sigma_0} =0.69. This yields a physical trajectory in the space of coupling cons…
