Weyl Anomaly of 2D Dilaton-Scalar Gravity and Hermiticity of System Operator

TL;DR

This paper investigates the Weyl anomaly in 2D dilaton-scalar gravity, focusing on how operator choice and measure definition affect the anomaly and the hermiticity of the system's operator.

Contribution

It clarifies the relationship between Weyl anomaly, operator choice, and hermiticity in 2D dilaton-scalar gravity using heat-kernel regularization.

Findings

Weyl anomaly depends on the differential operator and measure definition.

The arbitrariness in operator choice influences the anomaly calculation.

Hermiticity of the operator is examined in relation to anomaly and measure.

Abstract

Weyl Anomaly in the dilaton-scalar system in 2 dimensional gravity is examined. We take the heat-kernel regularization for the ultraviolet divergences. Generally the Weyl anomaly is determined by the 2nd order differential (elliptic) operator of the system and the definition of the measure. We have the freedom of the operator choice caused by the arbitrariness of total divergences (surface terms) in the action. We examine the Weyl anomaly in connection with such points and the hermiticity of the operator.