Non-Abelian anomalous constitutive relations of a chiral hadronic fluid

We study the constitutive relations of a chiral hadronic fluid in presence of non-Abelian’t Hooft anomalies. Analytical expressions for the covariant currents are obtained at first order in derivatives in the chiral symmetric phase, for both two and three quark flavors in the presence of chiral imbalance. We also investigate the constitutive relations after chiral symmetry breaking at the leading order.

An investigation of PT -symmetry breaking in tight-binding chains

We consider non-Hermitian PT -symmetric tight-binding chains where gain/loss optical potentials of equal magnitudes ±iγ are arbitrarily distributed over all sites. The main focus is on the threshold γ c beyond which PT -symmetry is broken. This threshold generically falls off as a power of the chain length, whose exponent depends on the configuration of optical potentials, ranging between 1 (for balanced periodic chains) and 2 (for unbalanced periodic chains, where each half of the chain experiences a non-zero mean potential). For random sequences of optical potentials with zero average and finite variance, the threshold is itself a random variable, whose mean value decays with exponent 3/2 and whose fluctuations have a universal distribution. The chains yielding the most robust PT -symmetric phase, i.e. the highest threshold at fixed chain length, are obtained by exact enumeration up to 48 sites. This optimal threshold exhibits an irregular dependence on the chain length, presumably decaying asymptotically with exponent 1, up to logarithmic corrections.

Gravitational waves generation in turbulent hypermagnetic fields before the electroweak phase transition

We study the production of relic gravitational waves (GWs) in turbulent hypermagnetic fields (HMFs) in the symmetric phase of the early universe before the electroweak phase transition (EWPT). The noise of HMFs is modeled by the analog of the magnetic hydrodynamics turbulence. The evolution of HMFs is driven by the analogs of the chiral magnetic effect and the Adler anomalies in the presence of the nonzero asymmetries of leptons and Higgs bosons. We track the evolution of the energy density of GWs from 10 TeV down to EWPT and analyze its dependence on the parameters of the system. We also discuss the possibility to observe the predicted GW background by the current GW detectors.

Gauge kinetic mixing and dark topological defects

We discuss how the topological defects in the dark sector affect the Standard Model sector when the dark photon has a kinetic mixing with the QED photon. In particular, we consider the dark photon appearing in the successive gauge symmetry breaking, SU(2) → U(1) → ℤ2, where the remaining ℤ2 is the center of SU(2). In this model, the monopole is trapped into the cosmic strings and forms the so-called bead solution. As we will discuss, the dark cosmic string induces the QED magnetic flux inside the dark string through the kinetic mixing. The dark monopole, on the other hand, does not induce the QED magnetic flux in the U(1) symmetric phase, even in the presence of the kinetic mixing. Finally, we show that the dark bead solution induces a spherically symmetric QED magnetic flux through the kinetic mixing. The induced flux looks like the QED magnetic monopole viewed from a distance, although QED satisfies the Bianchi identity everywhere, which we call a pseudo magnetic monopole.

Spectra, eigenstates and transport properties of a $\mathcal{PT}$-symmetric ring

We study, analytically and numerically, a simple $\mathcal{PT}$-symmetric tight-binding ring with an onsite energy $a$ at the gain and loss sites. We show that if $a\neq 0$, the system generically exhibits an unbroken PT -symmetric phase. We study the nature of the spectrum in terms of the singularities in the complex parameter space as well as the behavior of the eigenstates at large values of the gain and loss strength. We find that in addition to the usual exceptional points, there are “diabolical points”, and inverse exceptional points at which complex eigenvalues reconvert into real eigenvalues. We also study the transport through the system. We calculate the total flux from the source to the drain, and how it splits along the branches of the ring. We find that while usually the density flows from the source to the drain, for certain eigenstates a stationary “backflow” of density from the drain to the source along one of the branches can occur. We also identify two types of singular eigenstates, i.e. states that do not depend on the strength of the gain and loss, and classify them in terms of their transport properties.

Influence of the hypermagnetic field noise on the baryon asymmetry generation in the symmetric phase of the early universe

We study a matter turbulence caused by strong random hypermagnetic fields (HMFs) that influence the baryon asymmetry evolution due to the Abelian anomalies in the symmetric phase in the early Universe. Such a matter turbulence is stipulated by the presence of the advection term in the induction equation for which a fluid velocity is dominated by the Lorentz force in the Navier–Stokes equation. For random HMFs, having nonzero mean squared strengths, we calculate the spectra for the HMF energy and the HMF helicity densities. The latter function governs the evolution of the fermion asymmetries in the symmetric phase before the electroweak phase transition (EWPT). In the simplest model based on the first SM generation for the lepton asymmetries of $$e_\mathrm {R,L}$$ e R , L and $$\nu _{e_\mathrm {L}}$$ ν e L , we calculate a decline of all fermion asymmetries including the baryon asymmetry, given by the ‘t Hooft conservation law, when one accounts for a turbulence of HMFs during the universe cooling down to EWPT. We obtain that the stronger the mean squared strength of random initial HMFs is, the deeper the fermion asymmetries decrease, compared to the case in the absence of any turbulence.

PT-symmetry and supersymmetry: interconnection of broken and unbroken phases

The broken and unbroken phases of P T and supersymmetry in optical systems are explored for a complex refractive index profile in the form of a Scarf potential, under the framework of supersymmetric quantum mechanics. The transition from unbroken to the broken phases of P T -symmetry, with the merger of eigenfunctions near the exceptional point is found to arise from two distinct realizations of the potential, originating from the underlying supersymmetry. Interestingly, in P T -symmetric phase, spontaneous breaking of supersymmetry occurs in a parametric domain, possessing non-trivial shape invariances, under reparametrization to yield the corresponding energy spectra. One also observes a parametric bifurcation behaviour in this domain. Unlike the real Scraf potential, in P T -symmetric phase, a connection between complex isospecrtal superpotentials and modified Korteweg-de Vries equation occurs, only with certain restrictive parametric conditions. In the broken P T -symmetry phase, supersymmetry is found to be intact in the entire parameter domain yielding the complex energy spectra, with zero-width resonance occurring at integral values of a potential parameter.

Confinement-deconfinement transition and Z2 symmetry in Z2+Higgs theory

In this paper, we study the Polyakov loop and the [Formula: see text] symmetry in the lattice [Formula: see text] theory in four-dimensional space using Monte Carlo simulations. The results show that this symmetry is realized in the Higgs symmetric phase for large number of “temporal” lattice sites. To understand this dependence on the number of “temporal” sites, we consider a one-dimensional model by keeping terms of the original action corresponding to a single spatial site. In this approximation, the partition function can be calculated exactly as a function of the Polyakov loop. The resulting free energy is found to have the [Formula: see text] symmetry in the limit of large temporal sites. We argue that this is due to [Formula: see text] invariance as well as dominance of the distribution or density of states corresponding to the action.

Self-Organized PT-Symmetry of Exciton-Polariton Condensate in a Double-Well Potential

We investigate the dynamics and stationary states of a semiconductor exciton–polariton condensate in a double-well potential. We find that upon the population build-up of the polaritons by above-threshold laser pumping, coherence relaxation due to the phase fluctuations in the polaritons drives the system into a stable fixed point corresponding to a self-organized PT-symmetric phase.