We globally quench the theory of two dimensional massless fermions (many flavours) with quartic interactions by making the quartic coupling a smooth function of time. Working in a derivative expansion we show that the discrete Z2 symmetry in case of the Gross-Neveu model, and the U(1) symmetry in case of the Nambu-Jona-Lasinio model, are restored during the zero-temperature quench. For the Gross-Neveu model we show that this can be understood as an effective thermalization. The time of symmetry restoration shows scaling with the quench rate. We identify this with the Kibble-Zurek scaling in the problem. In a suitable double scaling limit, the symmetry restoration may be understood in terms of Liouville quantum mechanics.
We investigate the low temperature behavior of a system in a spontaneously broken symmetry phase described by an Euclidean quantum $λφ^{4}_{d+1}$ model with quenched disorder. Using a series representation for the averaged generating functional of connected correlation functions in terms of the moments of the partition function, we study the effects of the disorder linearly coupled to the scalar field. To deal with the strongly correlated disorder in imaginary time, we employthe equivalence between the model defined in a $d$-dimensional space with imaginary time with the statistical field theo…
We study the finite temperature symmetry behaviour of O(N_1) \times O(N_2) scalar models on the lattice and we prove that at sufficiently high temperatures and in arbitrary dimensions their full symmetry is always restored or, equivalently, that the phenomenon of Symmetry Non Restoration which, according to lowest order perturbation theory, takes place in the continuum version of these models, does not occur on the lattice.
We study symmetry of space-time in presence of a minimally coupled scalar field interacting with a Kalb--Ramond tensor fields in a homogeneous but initially anisotropic universe. The analysis is performed for the two relevant cases of a pure cosmological constant and a minimal quadratic, renormalizable, interaction term. In both cases, due to expansion, a complete spatial symmetry restoration is dynamically obtained.
We study the effect of next-to-leading order contributions on the phenomenon of symmetry non-restoration at high temperature in an $O(N_1)\times O(N_2)$ model.
This paper continues a study of field theories specified for the nonuniform lattice in the finite-dimensional hypercube with the use of the earlier described deformation parameters. The paper is devoted to spontaneous breakdown and restoration of symmetry in simple quantum-field theories with scalar fields. It is demonstrated that an appropriate deformation opens up new possibilities for symmetry breakdown and restoration. To illustrate, at low energies it offers high-accuracy reproducibility of the same results as with a nondeformed theory. In case of transition from low to higher energies an…
We investigate the effective potential for a scalar $Φ^{4}$ theory with spontaneous symmetry breaking at finite temperature. All 'daisy' and 'super daisy' diagrams are summed up and the properties of the corresponding gap eqation are investigated. It is shown exactly that the phase transition is first order.
We consider the one-loop effective potential at zero and finite temperature in field theories with anisotropic space-time scaling, with critical exponent $z=2$, including both scalar and gauge fields. Depending on the relative strength of the coupling constants for the gauge and scalar interactions, we find that there is a symmetry breaking term induced at one-loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature.
We study temperature and finite-size effects on the spontaneous symmetry breaking/restoration for a scalar field model under the influence of an external magnetic field, at finite chemical potential. We use the 2PI formalism and consider the large-$N$ limit. We find that there is a minimal size of the system to sustain the broken phase, which diminishes as the applied field increases but is independent of the chemical potential. We analyze the critical curves and show that the magnetic field enhances the broken-phase regions, while increasing the chemical potential leads to a diminishement of …
Chiral symmetry is dynamically broken in quenched, ladder QED at weak gauge couplings when an external magnetic field is present. In this paper, we show that chiral symmetry is restored above a critical chemical potential and the corresponding phase transition is of first order. In contrast, the chiral symmetry restoration at high temperatures (and at zero chemical potential) is a second order phase transition.
The restoration of spontaneous symmetry breaking for a scalar field theory for an accelerated observer is discussed by the one-loop effective potential calculation and by considering the effective potential for composite operators. Above a critical acceleration, corresponding to the critical restoration temperature,T_c, for a Minkowski observer by Unruh relation, i.e. a_c/2π=T_c, the symmetry is restored. This result confirms other recent calculations in effective field theories that symmetry restoration can occur for an observer with an acceleration larger than some critical value. From the p…
The one-loop effective potential for $ϕ^4$ theory on a Bianchi type-I universe is evaluated in the adiabatic approximation. It is used to see the quantum-field effects on symmetry breaking and restoration in anisotropic spacetimes. The results show that the fate of symmetry will not be changed in the cases of conformal coupling or a vanishing scale curvature, and only for some suitable values of scalar-gravitational coupling could the symmetry be radiatively broken or restored.
Based on the Hawking-Unruh thermalization theorem, we investigate the phenomenon of the dynamical chiral symmetry breaking and its restoration for a uniformly accelerated observer. We employ the Nambu$-$Jona-Lasinio model in Rindler coordinates, and calculate the effective potential and the gap equation. The critical coupling and the critical acceleration for symmetry restoration are obtained.
We overview two interconnected topics: possible effective restoration of chiral symmetry in highly excited hadrons and possible existence of confined but chirally symmetric matter at low temperatures and high densities.
Symmetry restoration is usually understood as a renormalization group induced phenomenon. In this context, the issue of whether one-loop RG equations can be trusted in predicting symmetry restoration has recently been the subject of much debate. Here we advocate a more pragmatic point of view and expand the definition of symmetry restoration to encompass all situations where the physical properties have only a weak dependence upon an anisotropy in the bare couplings. Moreover we concentrate on universal properties, and so take a scaling limit where the physics is well described by a field theo…
We show, without using semiclassical approximations, that, in high-temperature QCD with chiral symmetry restoration and U(1) axial symmetry breaking, the partition function for sufficiently light quarks can be expressed as an ensemble of noninteracting objects with topological charge that obey the Poisson statistics. We argue that the topological objects are "quasi-instantons" (rather than bare instantons) taking into account quantum effects. Our result is valid even close to the (pseudo)critical temperature of the chiral phase transition.
We consider the one-loop effective potential at zero and finite temperature in scalar field theories with anisotropic space-time scaling. For $z=2$, there is a symmetry breaking term induced at one-loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature. For $z=3$, we considered at first the case with a positive mass term at tree level and found no symmetry breaking effects induced at one-loop, and then we study the case with a negative mass term at tree level where we cannot conclude about symmetry restoration effects at high temper…
We reexamine a recently proposed non-inflationary solution to the monopole problem, based on the possibility that spontaneously broken Grand-Unified symmetries do not get restored at high temperature. We go beyond leading order by studying the self-consistent one-loop equations of the model. We find large next-to-leading corrections that reverse the lowest order results and cause symmetry restoration at high temperature.
The supergravity dual of $N$ regular and $M$ fractional D3-branes on the conifold has a naked singularity in the infrared. Supersymmetric resolution of this singularity requires deforming the conifold: this is the supergravity dual of chiral symmetry breaking. Buchel suggested that at sufficiently high temperature there is no need to deform the conifold: the singularity may be cloaked by a horizon. This would be the supergravity manifestation of chiral symmetry restoration. In previous work [hep-th/0102105] the ansatz and the system of second-order radial differential equations necessary to fi…
It is shown that in the large $N_c$ limit the light baryon spectrum exhibits the chiral restoration phase transition at high enough excitation energy. Such a phase transition is evidenced by the systematical parity doublets observed in the upper part of $N$ and $Δ$ spectra.
We study intersection of $N_c$ color D4 branes with $N_f$ Dp-branes and anti-Dp branes in the strong coupling limit in the probe approximation. The resulting model has $U(N_f)\times U(N_f)$ global symmetry. We see an $n$ dimensional theory for $n$ overlapping directions between color and flavor branes. At zero temperature we do see the breakdown of chiral symmetry, but there arises a puzzle: we do not see any massless NG boson to the break down of the chiral symmetry group for $n=2,3$ for a specific p. At finite temperature we do see the restoration of chiral symmetry group and the associated …
Exploiting the recent lattice results for the infrared gluon propagator with light dynamical quarks, we solve the gap equation for the quark propagator. We thus model the chiral symmetry breaking mechanism with increasing number of flavours and study confinement (intimately tied with the analytic properties of QCD Schwinger functions) order parameters. We obtain, with this approach, clear signals of chiral symmetry restoration and deconfinement when the number of light quark flavors exceeds a critical value of $N_f^c \approx 8 \pm 1$, in agreement with the state-of-the-art direct lattice analy…
We investigate numerically chiral symmetry restoration at finite temperature in the planar limit in the deconfined phase, both when it is stable and when the system is supercooled. We find chiral symmetry restoration at $T_χ= T_d$, where $T_d$ is the temperature of the deconfinement transition in pure gauge theory and $T_χ< T_d$ in the supercooled deconfined phase. In the stable case the spectrum of the Dirac operator opens a gap in a discontinuous manner and in the supercooled phase the gap seems to vanish continuously.
Dynamical spontaneous breaking of some discrete symmetries including special parities and time reversal and their restoration at finite temperature T are researched in 3D Gross-Neveu model by means of Schwinger-Dyson equation in the real-time thermal field theory in the fermion bubble diagram approximation. When the momentum cut-off $Λ$ is large enough, the equation of critical chemical potential $μ_c$ and critical temperature $T_c$ will be $Λ$-independent and identical to the one obtained by auxialiary scalar field approach. The dynamical fermion mass m, as the order parameter of symmetry bre…
We consider the massive vector $N$-component $(λφ^{4})_{D}$ theory defined on a Euclidean space with a toroidal topology. Using recently developed methods to perform a compactification of a $d$-dimensional subspace at finite chemical potential, we treat jointly the effects of temperature and spatial boundaries, setting forth grounds for an analysis of spontaneous symmetry restoration driven by temperature and spatial boundaries as a function of the chemical potential. We restrict ourselves to d=2, which corresponds to the heated system confined between two parallel planes (separation $L$) in d…
We study the Z_N symmetry in SU(N)+Higgs theories with the Higgs field in the fundamental representation. The distributions of the Polyakov loop show that the Z_N symmetry is explicitly broken in the Higgs phase. On the other hand, inside the Higgs symmetric phase the Polyakov loop distributions and other physical observables exhibit the Z_N symmetry. This effective restoration of the Z_N symmetry changes the nature of the confinement-deconfinenement transition. We argue that the Z_N symmetry will lead to time independent topological defect solutions in the Higgs symmetric deconfined phase whi…
A four-fermion model with additional higher-derivative terms is investigated in an external electromagnetic field. The effective potential in the leading order of large-N expansion is calculated in external constant magnetic and electric fields. It is shown that, in contrast to the former results concerning the universal character of "magnetic catalysis" in dynamical symmetry breaking, in the present higher-derivative model the magnetic field restores chiral symmetry broken initially on the tree level. Numerical results describing a second-order phase transition that accompanies the symmetry r…
We study the role played by a Chern-Simons contribution to the action in the $QED_3$ formulation of a two-dimensional Heisenberg model of quantum spin systems with a strictly fixed site occupation at finite temperature. We show how this contribution affects the screening of the potential which acts between spinons and contributes to the restoration of chiral symmetry in the spinon sector. The constant which characterizes the Chern-Simons term can be related to the critical temperature $T_c$ above which the dynamical mass goes to zero.
We explore the conditions for chiral symmetry breaking in reduced (or pseudo) quantum electrodynamics at finite temperature in connection with graphene and other 2D-materials with an underlying Dirac behavior of the charge carriers. By solving the corresponding Schwinger-Dyson equation in rainbow approximation, in a Landau-like gauge and neglecting wavefunction renormalization effects, we find the need of the coupling to exceed a critical value $α_c$ in order for chiral symmetry to be broken, in agreement with known results from other groups. In this supercritical regime, we add the effects of…
For 1 Dimensional loop space, a nonlinear nonlocal transformation of fields is given to make the action of the self-interacting quantum field to the free one. A specific type of Classically broken symmetry is restored in Quantum theory. 1-D Sine Gordon system and Sech interactions are treated as the explicit example.
A finite volume allows tunnelling between degenerate vacua in Quantum Field Theory, and leads to remarkable energetic features, arising from the competition of different saddle points in the partition function. We describe this competition for finite temperature at equilibrium, taking into account both static and (Euclidean) time-dependent saddle points. The effective theory for the homogeneous order parameter yields a non-extensive vacuum energy at low temperatures, implying a dynamical violation of the Null Energy Condition.
Physics of the low-lying and high-lying hadrons in the light flavor sector is reviewed. While the low-lying hadrons are strongly affected by the spontaneous breaking of chiral symmetry, in the high-lying hadrons the chiral symmetry is restored. A manifestation of the chiral symmetry restoration in excited hadrons is a persistence of the chiral multiplet structure in both baryon and meson spectra. Meson and baryon chiral multiplets are classified. A relation between the chiral symmetry restoration and the string picture of excited hadrons is discussed.
We study symmetry restoration at finite temperature in the standard model during the electroweak phase transition in the presence of a weak magnetic field. We compute the finite temperature effective potential up to the contribution of ring diagrams, using the broken phase degrees of freedom, and keep track of the gauge parameter dependence of the results. We show that under these conditions, the phase transition becomes stronger first order.
In the multiverse, the universes can be created in entangled pairs with spacetimes that are both expanding in terms of the time variables experienced by internal observers in their particle physics experiments. The time variables of the two universes are related by an antipodal-like symmetry that might explain why there is no antimatter in our universe: at the origin, antimatter is created, by definition and for any observer, in the observer's partner universe. The Euclidean region of the spacetime that separates the two universes acts as a quantum barrier that prevents matter-antimatter from …
We present and analyze a new set of Ward Identities which shed light on the distinction between different patterns of chiral symmetry restoration in QCD, namely $O(4)$ vs $O(4)\times U(1)_A$. The degeneracy of chiral partners for all scalar and pseudoscalar meson nonet members are studied through their corresponding correlators. Around chiral symmetry degeneration of $O(4)$ partners, our analysis predicts that $U(1)_A$ partners are also degenerated. Our analysis also leads to $I=1/2$ scalar-pseudoscalar partner degeneration at exact chiral restoration, and supports ideal mixing between the $η$…
Quenched SU(3) lattice gauge theory shows three phase transitions, namely the chiral, the deconfinement and the Z3 phase transition. Knowing whether or not the chiral and the deconfinement phase transition occur at the same temperature for all Z3 sectors could be crucial to understand the underlying microscopic dynamics. We use the existence of a gap in the Dirac spectrum as an order parameter for the restoration of chiral symmetry. We find that the spectral gap opens up at the same critical temperature in all Z3 sectors in contrast to earlier claims in the literature.
We propose a scenario where superheavy dark matter (DM) can be produced via symmetry restoration first-order phase transition during inflation triggered by the evolution of the inflaton field. The phase transition happens in a spectator sector coupled to the inflaton field. During the phase transition, the spectator field tunnels from a symmetry-broken vacuum to a symmetry-restored vacuum. The massive particles produced after bubble collisions are protected against decaying by the restored symmetry and may serve as a DM candidate in the later evolution of the Universe. We show that the latent …
We demonstrate that chiral symmetry restoration in quenched finite temperature QCD depends crucially on the $Z_3$ phase of the Polyakov loop ${\cal P}$. This dependence is a general consequence of the coupling of the chiral order parameter to the Polyakov loop. We construct a model for chiral symmetry breaking and restoration which includes the effect of a nontrivial Polyakov loop by calculating the effective potential for the chiral condensate of a Nambu-Jona-Lasinio model in a uniform temperature dependent $A_0$ gauge field background. Above the deconfinement temperature there are three poss…
A fast restoration of chiral symmetry in excited mesons is demonstrated. A minimal "realistic" chirally symmetric confining model is used, where the only interaction between quarks is the linear instantaneous Lorentz-vector confining potential. Chiral symmetry breaking is generated via the nonperturbative resummation of valence quarks self-energy loops and the meson bound states are obtained from the Bethe-Salpeter equation. The excited mesons fall into approximate chiral multiplets and lie on the approximately linear radial and angular Regge trajectories, though a significant deviation from t…
We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.
In this paper, we discuss the transition to the semiclassical regime in excited hadrons, and consequently, the restoration of chiral symmetry for these states. We use a generalised Nambu-Jona-Lasinio model with the interaction between quarks in the form of the instantaneous Lorentz-vector confining potential. This model is known to provide spontaneous breaking of chiral symmetry in the vacuum via the standard selfenergy loops for valence quarks. It has been shown recently that the effective single-quark potential is of the Lorentz-scalar nature, for the low-lying hadrons, while, for the high-l…
We analyze the chiral phase transition of the Nambu--Jona-Lasinio model in the cold and dense region on the lattice developing the Grassmann version of the anisotropic tensor renormalization group algorithm. The model is formulated with the Kogut--Susskind fermion action. We use the chiral condensate as an order parameter to investigate the restoration of the chiral symmetry. The first-order chiral phase transition is clearly observed in the dense region at vanishing temperature with $μ/T\sim O(10^3)$ on a large volume of $V=1024^4$. We also present the results for the equation of state.
