There exists a large class of models which are self-dual with respect to inversion of coupling constants. When a theta term is added, this duality may be extended to an invariance under an action of an infinite discrete modular group on the coupling parameter space. In particular, four-dimensional abelian lattice gauge theories possess a Sp(2k, Z) modular symmetry, where k is the number of simple factors in the gauge group. We generalize this result to models of arbitrary dimension, and show that the partition functions of two-dimensional ZN spin models with 2k flavors and string compactifications on k-dimensional tori are invariant under O(k, k; Z). We also draw some suggestive parallels to the fractional quantum Hall effect.
ASJC Scopus subject areas
- Nuclear and High Energy Physics