Anomalies and the Helicity of the Thermal State

TL;DR

This paper investigates the thermal helicity in quantum field theories, proposing it as a polynomial in temperature and chemical potential linked to anomalies, supported by computations in free theories.

Contribution

It introduces the concept of thermal helicity and conjectures its relation to anomaly polynomials, connecting thermal expectation values to gravitational anomalies.

Findings

Thermal helicity per unit volume is a polynomial in T and μ.

In theories without chiral gravitino, this polynomial derives from the anomaly polynomial.

Supports conjecture with sphere partition function computations in free theories.

Abstract

We study the thermal expectation value of the following observeable at finite temperature T and chemical potential \mu : < L_{12} L_{34} ... L_{d-3,d-2} P_{d-1} > where L_{ij} denote the angular momenta, and P_i denotes the spatial momentum in d spacetime dimensions with d even. We call this observeable the thermal helicity. Using a variety of arguments, we motivate the surprising assertion that thermal helicity per unit volume is a polynomial in T and \mu. Further, in field theories without chiral gravitino, we conjecture that this polynomial can be derived from the anomaly polynomial of the theory. We show that this conjecture is related to the recent conjecture on gravitational anomaly induced transport made in arXiv:1201.2812 . We support these statements by various sphere partition function computations in free theories.