Flux compactifications of Type II string theories under non-perturbative dualities

Abstract

We consider string vacua formed by compactifying Type II string theories on toroidal orbifolds and generalised Calabi-Yau manifolds and their transformations under a set of non-perturbative dualities. The dualities are the Type IIA-IIB exchanging T duality, the self-symmetry of Type IIB S duality, the non-trivial combination of the two, U duality, and the generalisation of T duality to include Calabi-Yaus, mirror symmetry. The requirement of the effective theory superpotential being invariant under these dualities is used to justify additional fluxes which do not descend via compactification from the ten dimensional action, which form an N = 2 theory. Their non-geometric structures, Bianchi constraints and tadpoles are determined and then classified in terms of modular S duality induced multiplets. The Z2 Z2 orientifold is used as an explicit example of the general methods, with N = 1 Type IIB non-geometric vacua which possess T and S duality invariance also constructed. These are then used to motivate the existence of an exchange between moduli spaces on self mirror dual manifolds with N = 2. Such an exchange is seen to result in flux structures which are schematically the same as the standard formulation but with inequivalent flux constraints.

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