The Conformal Anomaly in General Rank 1 Symmetric Spaces and Associated Operator Product

TL;DR

This paper calculates the one-loop effective action and conformal anomaly for Laplace-type operators on rank 1 symmetric spaces, providing explicit formulas for zeta functions and stress-energy tensor anomalies.

Contribution

It introduces explicit computations of the conformal anomaly and zeta functions for operators on non-compact rank 1 symmetric spaces, advancing understanding of quantum effects in these geometries.

Findings

Explicit formulas for zeta functions derived.

Conformal anomaly of stress-energy tensor computed.

Effective action characterized for specific symmetric spaces.

Abstract

We compute the one-loop effective action and the conformal anomaly associated with the product $\bigotimes_p{\cal L}_p$ of the Laplace type operators ${\cal L}_p, p=1,2$, acting in irreducible rank 1 symmetric spaces of non-compact type. The explicit form of the zeta functions and the conformal anomaly of the stress-energy momentum tensor is derived.