The boundary effect of anomaly-induced action

TL;DR

This paper investigates how boundary effects influence the anomaly-induced action in two-dimensional spacetime, revealing that classical auxiliary fields can encode quantum states when boundary conditions are properly considered.

Contribution

It clarifies the relationship between auxiliary scalar fields and quantum states by incorporating boundary effects, which was previously overlooked in studies of anomaly-induced actions.

Findings

Boundary effects connect classical auxiliary fields to quantum states.

Solutions in flat, black hole, and de Sitter spacetimes illustrate this relationship.

Abstract

We discuss the boundary effect of anomaly-induced action in two-dimensional spacetime, which is ignored in previous studies. Anomaly-induced action, which gives the stress tensor with the same trace as the trace anomaly, can be represented in terms of local operators by introducing an auxiliary scalar field. Although the degrees of freedom of the auxiliary field can in principle describe the quantum states of the original field, the principal relation between them was unclear. We show here that, by considering the boundary effect, the solutions of classical auxiliary fields are naturally related to the quantum states of the original field. We demonstrate this conclusion via several examples such as the flat, black hole and the de Sitter spacetime.