Finiteness of Flux Vacua from Geometric Transitions

TL;DR

This paper demonstrates the finiteness of flux vacua near type IIB Calabi-Yau singularities by analyzing gauge theory duals, geometric transitions, and S duality, supported by explicit calculations at key singular points.

Contribution

It introduces a geometric transition framework linking flux vacua to gauge theory duals, establishing finiteness through holomorphic coupling changes and duality symmetries.

Findings

Finiteness of flux vacua proven near CY singularities.

Matching vacuum counts at conifold and Argyres-Douglas points.

Validation of the geometric transition and duality approach.

Abstract

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.