Anomaly inflow and thermal equilibrium

Kristan Jensen,Amos Yarom,R Loganayagam

doi:10.1007/jhep05(2014)134

Abstract

Using the anomaly inflow mechanism, we compute the flavor/Lorentz non-invariant contribution to the partition function in a background with a U(1) isometry. This contribution is a local functional of the background fields. By identifying the U(1) isometry with Euclidean time we obtain a contribution of the anomaly to the thermodynamic partition function from which hydrostatic correlators can be efficiently computed. Our result is in line with, and an extension of, previous studies on the role of anomalies in a hydrodynamic setting. Along the way we find simplified expressions for Bardeen-Zumino polynomials and various transgression formulae

Highlights

Anomalies are a fascinating and unavoidable feature of quantum field theory
By identifying the U(1) isometry with Euclidean time we obtain a contribution of the anomaly to the thermodynamic partition function from which hydrostatic correlators can be efficiently computed
Little is known about the effect of anomalies in thermodynamic states or in configurations which are close to thermodynamic equilibrium

Summary

Introduction

Anomalies are a fascinating and unavoidable feature of quantum field theory. Their presence has been studied in great detail over the last forty-odd years leading to an improved understanding of the behavior of quantum field theories in general (via, e.g., the ‘t Hooft anomaly matching condition, or the Green-Schwarz mechanism) in addition to observable phenomena as predicted by the standard model (such as the pion decay rate). All of the anomaly-induced response studied in the literature can be characterized by its effect on correlation functions in a hydrostatic configuration i.e., by its effect on variations of WQFT with respect to the background gauge field and metric.. One can argue that the zero frequency two point function of the covariant current and stress tensor of a 3 + 1 dimensional theory with a U(1) anomaly characterized by a coefficient cA and. As argued by Bardeen and Zumino [37], one may always construct a covariant stress tensor and current by adding appropriate compensating currents TBμZν and JBμZ which are polynomials in the connections and field strengths, TPμν = Taμnνom + TBμZν. A second construction which we elaborate on in this paper allows us to obtain the covariant anomaly-induced stress tensor and current, TPμν and JPμ without carrying out the explicit variation of Wanom. Many of the technical details have been relegated to the appendices

A minimalist’s introduction to hydrostatics

Partition functions for theories with abelian anomalies

Abelian anomaly-induced transport