Discrete Symmetries of Functional Determinants

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.

18 pages

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• The Dirac Operator in a Fermion Bag Background in 1+1 Dimensions and Generalized Supersymmetric Quantum Mechanics
• Spectral geometry for strings and branes
• Divergence terms in the supertrace heat asymptotics for the de Rham complex on a manifold with boundary
• Supertrace divergence terms for the Witten Laplacian