Abelian Duality

Abstract

We show that on three-dimensional Riemannian manifolds without boundaries and with trivial first real de Rham cohomology group (and in no other dimensions) scalar field theory and Maxwell theory are equivalent: the ratio of the partition functions is given by the Ray-Singer torsion of the manifold. On the level of interaction with external currents, the equivalence persists provided there is a fixed relation between the charges and the currents.

11 pages, LaTeX, no figures, a reference added, submitted to Phys. Rev. D

References in corpus (5)

• Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue
• Gauge Invariance, Finite Temperature and Parity Anomaly in D=3
• Induced Parity Breaking Term at Finite Temperature
• Abelian and Non-Abelian Induced Parity Breaking Terms at Finite Temperature
• Equivalence of the Self-Dual Model and Maxwell-Chern-Simons Theory on Arbitrary Manifolds

Cited by in corpus (5)

• Superconformal index on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ and mirror symmetry
• Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality
• Abelian Duality for Generalised Maxwell Theories
• Abelian duality in three dimensions
• Generalized Kodama partition functions: A preview into normalizability for the generalized Kodama states