Finiteness of Flux Vacua from Geometric Transitions

GONZALO TORROBA

JOURNAL OF HIGH ENERGY PHYSICS - (Online)

IOP Science

Año: 2007 vol. 2007 p. 1 - 25

1029-8479

We argue for finiteness of flux vacua around type IIB CY singularities by computing their gauge theory duals. This leads us to propose a geometric transition where the compact 3-cycles support both RR and NS flux, while the open string side contains 5-brane bound states. By a suitable combination of S duality and symplectic transformations, both sides are shown to have the same IR physics. The finiteness then follows from a holomorphic change of couplings in the gauge side. As a nontrivial test, we compute the number of vacua on both sides for the conifold and the Argyres-Douglas point, and we find perfect agreement.