Generalized Virasoro anomaly and stress tensor for dilaton coupled theories

TL;DR

This paper generalizes the Virasoro anomaly for 2D scalar fields coupled to a dilaton, deriving a consistent transformation law for the quantum stress tensor and applying it to curved backgrounds to analyze phenomena like Hawking radiation.

Contribution

It introduces a generalized anomalous transformation law for the stress tensor in dilaton-coupled theories, extending the Virasoro anomaly to include dilaton effects.

Findings

Derived a consistent stress tensor transformation law for dilaton-coupled theories.

Applied the law to compute stress tensor expectation values on curved backgrounds.

Provided insights into vacuum polarization and Hawking radiation effects.

Abstract

We derive the anomalous transformation law of the quantum stress tensor for a 2D massless scalar field coupled to an external dilaton. This provides a generalization of the Virasoro anomaly which turns out to be consistent with the trace anomaly. We apply it together with the equivalence principle to compute the expectation values of the covariant quantum stress tensor on a curved background. Finally we briefly illustrate how to evaluate vacuum polarization and Hawking radiation effects from these results.