Resolving spacetime singularities in flux compactifications & KKLT

TL;DR

This paper proposes a non-perturbative resolution to spacetime singularities near seven-branes in flux compactifications, ensuring the validity of KKLT de Sitter vacua by employing exotic branes and Argyres-Douglas theories.

Contribution

It introduces a non-perturbative framework using exotic branes and Argyres-Douglas theories to resolve singularities in flux compactifications, preserving KKLT effective field theory.

Findings

Wrapped seven-branes can be viewed as bound states of exotic branes.

Non-perturbative splitting of seven-branes resolves pathological regions.

Small flux superpotential maintains KKLT validity despite large pathological regions.

Abstract

In flux compactifications of type IIB string theory with D3 and seven-branes, the negative induced D3 charge localized on seven-branes leads to an apparently pathological profile of the metric sufficiently close to the source. With the volume modulus stabilized in a KKLT de Sitter vacuum this pathological region takes over a significant part of the entire compactification, threatening to spoil the KKLT effective field theory. In this paper we employ the Seiberg-Witten solution of pure $SU(N)$ super Yang-Mills theory to argue that wrapped seven-branes can be thought of as bound states of more microscopic exotic branes. We argue that the low-energy worldvolume dynamics of a stack of $n$ such exotic branes is given by the $(A_1,A_{n-1})$ Argyres-Douglas theory. Moreover, the splitting of the perturbative (in $\alpha'$) seven-brane into its constituent branes at the non-perturbative level resolves the apparently pathological region close to the seven-brane and replaces it with a region of $\mathcal{O}(1)$ Einstein frame volume. While this region generically takes up an $\mathcal{O}(1)$ fraction of the compactification in a KKLT de Sitter vacuum we argue that a small flux superpotential \textit{dynamically} ensures that the 4d effective field theory of KKLT remains valid nevertheless.