Massive-Scalar Effective Actions on Anti-de Sitter Spacetime

TL;DR

This paper derives explicit formulas for the effective actions of free massive scalar fields in anti-de Sitter spacetime across various dimensions, challenging a recent duality proposal.

Contribution

It provides closed-form expressions for effective actions in AdS for arbitrary dimensions, using elementary and Gamma functions, and questions a recent duality conjecture.

Findings

Explicit effective action formulas for odd and even dimensions.

Arguments against the quantum validity of a recent duality.

Simplified expressions using elementary and Gamma functions.

Abstract

Closed forms are derived for the effective actions for free, massive spinless fields in anti-de Sitter spacetimes in arbitrary dimensions. The results have simple expressions in terms of elementary functions (for odd dimensions) or multiple Gamma functions (for even dimensions). We use these to argue against the quantum validity of a recently-proposed duality relating such theories with differing masses and cosmological constants.