Multicritical microscopic spectral correlators of hermitian and complex matrices

The replica limit of unitary matrix integrals

We examine random matrix models of QCD which are capable of supporting both chiral and diquark condensation. A numerical study of the spectral densities near zero virtuality shows that the introduction of color in the interactions does not alter the one-body results imposed by chiral symmetry. A model with three colors has the spectral density predicted for the chiral ensemble with a Dyson index $\ensuremath{\beta}=2;$ a pseudoreal model with two colors exhibits the spectral density of the chiral ensemble with $\ensuremath{\beta}=1.$

Spontaneous chiral symmetry breaking in QCD with massless quarks at infinite volume can be seen in a finite box by studying, for instance, the dependence of the chiral condensate from the volume and the quark mass. We perform a feasibility study of this program by computing the quark condensate on the lattice in the quenched approximation of QCD at small quark masses. We carry out simulations in various topological sectors of the theory at several volumes, quark masses and lattice spacings by employing fermions with an exact chiral symmetry, and we focus on observables which are infrared stable and free from mass-dependent ultraviolet divergences. The numerical calculation is carried out with an exact variance-reduction technique, which is designed to be particularly efficient when spontaneous symmetry breaking is at work in generating a few very small low-lying eigenvalues of the Dirac operator. The finite-size scaling behaviour of the condensate in the topological sectors considered agrees, within our statistical accuracy, with the expectations of the chiral effective theory. Close to the chiral limit we observe a detailed agreement with the first Leutwyler-Smilga sum rule. By comparing the mass, the volume and the topology dependence of our results with the predictions of the chiral effective theory, we extract the corresponding low-energy constant.

The microscopic spectral correlations of the Dirac operator in Yang-Mills theories coupled to fermions in $2+1$ dimensions can be related to three universality classes of random matrix theory. In the microscopic limit the orthogonal ensemble corresponds to a theory with two colors and fermions in the fundamental representation and the symplectic ensemble corresponds to an arbitrary number of colors and fermions in the adjoint representation. Using the new method of Widom, we derive an expression for the two scalar kernels which through quaternion determinants gives all spectral correlation functions in the Gaussian orthogonal ensemble (GOE) and in the Gaussian symplectic ensemble (GSE) with all fermion masses equal to zero. The result for the GOE is valid for an arbitrary number of fermions while for the GSE we have results for an even number of fermions.

Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks – Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss – Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.

This paper presents our study of the presence of the unstable critical point in spontaneous symmetry breaking (SSB) in the framework of Ginzburg–Landau (G-L) free energy. Through a 3D Ising spin lattice simulation, we found a zone of hysteresis where the unstable critical point continued to exist, despite the system having entered the broken symmetry phase. Within the hysteresis zone, the presence of the kink–antikink SSB solitons expands and, therefore, these can be observed. In scalar field theories, such as Higgs fields, the mass of this soliton inside the hysteresis zone could behave as a tachyon mass, namely as an imaginary quantity. Due to the fact that groups Ζ(2) and SU(2) belong to the same universality class, one expects that, in future experiments of ultra-relativistic nuclear collisions, in addition to the expected bosons condensations, structures of tachyon fields could appear.

We show that exotic spontaneous symmetry breaking appears in thermal topological phases by perturbing the exact solutions of quantum rotor models coupled to the three-dimensional toric code. The exotic Ising and XY transitions are shown to be in the same universality class, in drastic contrast to the conventional Wilson-Fisher classes without topological orders. Our results indicate that topological orders must be included to pin down the universality classes of thermal transitions in addition to order parameter symmetry and spatial dimension. We evaluate all the critical exponents and find that the exotic universality class is more stable under the couplings to acoustic phonons and disorder. Applying our results to experiments, we provide a plausible scenario in puzzlings of strongly correlated systems, including the absence of a specific heat anomaly in doped ${\mathrm{RbFe}}_{2}{\mathrm{As}}_{2}$.

Spontaneous chiral symmetry breaking is a ubiquitous property in nature and diverse fields of modern physics. However, such symmetry breaking has been elusive experimentally in the optical systems, which usually demands multiple identical subsystems [1]. As a prominent photonic device, the ultrahigh-Q whispering-gallery mode (WGM) microresonator supports clockwise (CW) and counterclockwise (CCW) propagating waves coupled to each other, leading to symmetric and antisymmetric standing-wave modes with equal CW and CCW amplitudes. The demonstrations of such overall chirality have to rely on external perturbations to a resonator, either by breaking the parity or time-reversal symmetry [2,3]. The chirality with unbalanced CW and CCW components not only attracts general interest in physics, but also is of importance in novel devices [2,3]. Here, we experimentally demonstrate the spontaneous chirality in a single WGM microresonator (Fig. 1) without any explicit breaking of parity or time-reversal symmetry.

Phase structure of quantum electrodynamics in the framework of the Schwinger-Dyson equation

An analysis of the spontaneous breaking of chiral symmetry in three dimensional electrodynamics is described. It is argued that this model, when treated in a 1/ N expansion, does exhibit spontaneous chiral symmetry breaking. This is established by finding analytic and numer· ical solutions to the Dyson-Schwinger equation and then computing the composite-operator effective potential. During the fifty years since Y uka wa proposed the J[ meson as the intermediary of nuclear forces, our view of this particle has continued to evolve. We now know it to be a quark-antiquark composite, and in quantum chromodynamics, QCD, we have a strong interaction theory that may well describe its dynamics and that of the other hadrons. Among all the hadrons, however, the 1f meson is believed to play a special role. The underlying theory of strong interactions posseses a near chiral symmetry, SU(2h X SU(2) R, because of the approximate masslessness of the up and down quarks. This symmetry must then break spontaneously in order to explain the effective 300 MeV masses that these quarks appear to possess as the constituents of hadrons. The spontaneous breaking of any continuous symmetry necessarily leads to the existence of massless Goldstone bosons, and in the case of chiral symmetry, the 1f mesons approximately play this role. The small bare mass of the up and down quarks leads to a small mass for 1f mesons 1

The spontaneous breaking of chiral symmetry is examined by chiral effective theories, such as the linear $\sigma$ model and the Nambu–Jona-Lasinio (NJL) model. We discuss the properties of the sigma meson regarded as the quantum fluctuation of the chiral condensate when the chiral symmetry is spontaneously broken, mainly by the U$_{A}$(1) anomaly. We derive a mass relation among the SU(3) flavor singlet mesons, $\eta_{0}$ and $\sigma_{0}$, in the linear $\sigma$ model to be satisfied for the anomaly-driven symmetry breaking in the chiral limit, and find that it is also supported in the NJL model. With the explicit breaking of chiral symmetry, we show that both of the chiral effective models reproducing the observed physical quantities suggest that the $\sigma_{0}$ meson should have a mass smaller than $\sim$800 MeV when anomaly-driven symmetry breaking takes place.

We study NfD6-brane probes in the supergravity background dual to NcD4-branes compactified on a circle with supersymmetry-breaking boundary conditions. In the limit in which the resulting Kaluza-Klein modes decouple, the gauge theory reduces to non-supersymmetric, four-dimensional QCD with Nc colours and Nf << Ncflavours. As expected, this decoupling is not fully realised within the supergravity/Born-Infeld approximation. For Nf = 1 and massless quarks, mq = 0, we exhibit spontaneous chiral symmetry breaking by a quark condensate, ⟨ψ⟩≠0, and find the associated massless `pion' in the spectrum. The latter becomes massive for mq > 0, obeying the Gell-Mann-Oakes-Renner relation: Mπ2 = −mq ⟨ψ⟩/fπ2. In the case Nf>1 we provide a holographic version of the Vafa-Witten theorem, which states that the U(Nf) flavour symmetry cannot be spontaneously broken. Further, we find Nf2−1 unexpectedly light pseudo-scalar mesons in the spectrum. We argue that these are not (pseudo-)Goldstone bosons and speculate on the string mechanism responsible for their lightness. We then study the theory at finite temperature and exhibit a phase transition associated with a discontinuity in ⟨ψ⟩(T). D6/ pairs are also briefly discussed.

We test a candidate for a four-dimensional C function. This is done by considering all asymptotically free, vectorlike gauge theories with ${N}_{f}$ flavors and fermions in arbitrary representations of any simple Lie group. Assuming spontaneous breaking of chiral symmetry in the infrared limit and that the value of the C function in this limit is determined by the number of Goldstone bosons, we find that only in the case of a theory with two colors and fermions in one single pseudoreal representation of SU(2) does the C theorem seem to be violated. Conversely, this might also be a sign of new constraints, restricting the number of flavors consistent with spontaneous chiral symmetry breaking. For all other groups and representations we find that this candidate C function decreases along the renormalization-group flow.

Spontaneous chiral symmetry breaking underpins a variety of areas such as subatomic physics and biochemistry, and leads to an impressive range of fundamental phenomena. Here we show that this prominent effect is now available in artificial electromagnetic systems, enabled by the advent of magnetoelastic metamaterials where a mechanical degree of freedom leads to a rich variety of strong nonlinear effects such as bistability and self-oscillations. We report spontaneous symmetry breaking in torsional chiral magnetoelastic structures where two or more meta-molecules with opposite handedness are electromagnetically coupled, modifying the system stability. Importantly, we show that chiral symmetry breaking can be found in the stationary response of the system, and the effect is successfully demonstrated in a microwave pump-probe experiment. Such symmetry breaking can lead to a giant nonlinear polarization change, energy localization and mode splitting, which provides a new possibility for creating an artificial phase transition in metamaterials, analogous to that in ferrimagnetic domains.

It has been recently pointed out by Mithani-Vilenkin [1-4] that certain emergent universe scenarios which are classically stable are nevertheless unstable semiclassically to collapse. Here, we show that there is a class of emergent universes derived from scale invariant two measures theories with spontaneous symmetry breaking (s.s.b) of the scale invariance, which can have both classical stability and do not suffer the instability pointed out by Mithani-Vilenkin towards collapse.We find that this stability is due to the presence of a symmetry in the “emergent phase”, which together with the non linearities of the theory, does not allow that the FLRW scale factor to be smaller that a certain minimum value a0 in a certain protected region.