Chirality dependence in charge and heat transport in thermal QCD

TL;DR

This paper investigates how weak magnetic fields influence charge and heat transport in thermal QCD, revealing chiral-dependent Hall effects and violations of the Wiedemann-Franz law through a kinetic theory approach.

Contribution

It introduces a kinetic theory framework with chiral mass differences to study tensorial conductivities and derives new coefficients like the Hall conductivities and Lorenz numbers in thermal QCD.

Findings

Lorenz number varies with magnetic field and chiral mode.

Hall conductivities depend on magnetic field and chiral mode.

Wiedemann-Franz law is violated in this context.

Abstract

In the presence of weak magnetic field ($B$), novel phenomena, similar to Hall effect in condensed matter physics, emerge both in charge and heat transport in a thermal QCD medium. Here, we have employed the kinetic theory approach within a quasiparticle framework, wherein the effective masses for left (L) and right-handed (R) chiral modes of quarks are seen different, lifting the prevalent degeneracy. Another implication of weak $B$ is that the coefficients assume a tensorial structure: The diagonal elements represent the usual conductivities: $\sigma_{\text{Ohmic}}$ and $\kappa_0$ as the coefficients of charge and heat transport, respectively and the off-diagonal elements denote their Hall counterparts: $\sigma_{\text{Hall}}$ and $\kappa_1$, respectively. Finally, we have derived some coefficients, namely, the Knudsen number and Lorenz number in Wiedemann-Franz law. Lorenz number and Hall-Lorenz number for L-mode increases and for R-mode decreases with a magnetic field. it does not remain constant with $T$ hence violating the Wiedemann-Franz law.