## Abstract

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 Z_{N} 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.

Original language | English |
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Pages (from-to) | 669-695 |

Number of pages | 27 |

Journal | Nuclear Physics B |

Volume | 320 |

Issue number | 3 |

DOIs | |

State | Published - Jul 10 1989 |

### Bibliographical note

Funding Information:We thank J. Cardy, B. Halperin, R. MacKenzie, and C. Vafa for helpful conversations. Special thanks go to V. P. Nair for his role in the early stages of this research. This work was supported in part by the Department of Energy under Grant. No. DE-AC02-76ERO-2220 and by the National Science Foundation under Grants No. PHY-87-14654 and PHY-82-17853, supplemented by funds from the National Aeronautics and Space Administration.

## ASJC Scopus subject areas

- Nuclear and High Energy Physics