Modular Invariance of Field Theories and String Compactifications
There is a large class of Gaussian lattice models which are self-dual with respect to inversion of coupling constants. When a theta term is added, this duality may extend to an invariance under an action of an infinite discrete modular group on the coupling parameter space. In particular, 4-dimensional Abelian lattice gauge theories possess a Sp(2k, Z) modular symmetry, and string compactifications on d-dimensional tori are invariant under SO(16 + d, d; Z). We review these results and their applications, and discuss the classification of self-dual string compactifications.
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