Discrete Symmetries of Functional Determinants

TL;DR

This paper investigates discrete duality symmetries of functional determinants, revealing exact transformations under background field inversion and identifying cases where determinants remain invariant, with implications for string theory and black holes.

Contribution

It introduces an exact transformation of the effective action under background field inversion and demonstrates invariance of functional determinants in various models.

Findings

Inversion of background fields often leaves determinants unchanged.

Explicit models show invariance under duality transformations.

Results connect strong and weak coupling regimes in theoretical physics.

Abstract

We study discrete (duality) symmetries of functional determinants. An exact transformation of the effective action under the inversion of background fields $\beta (x) \to \beta^{-1}(x)$ is found. We show that in many cases this inversion does not change functional determinants. Explicitly studied models include a matrix theory in two dimensions, the dilaton-Maxwell theory in four dimensions on manifolds without a boundary, and a two-dimensional dilaton theory on manifolds with boundaries. Our results provide an exact relation between strong and weak coupling regimes with possible applications to string theory, black hole physics and dimensionally reduced models.