Enumerating Flux Vacua with Enhanced Symmetries

TL;DR

This paper investigates the distribution and properties of flux vacua in type IIB string theory, focusing on vacua with special symmetries and their growth rate, using both statistical and number-theoretic methods.

Contribution

It introduces new number-theoretic techniques to analyze flux vacua and compares these results with existing statistical predictions.

Findings

Vacua with W=0 have specific distribution patterns.

The growth rate of vacua matches statistical predictions.

Elementary number-theoretic methods effectively analyze flux vacua properties.

Abstract

We study properties of flux vacua in type IIB string theory in several simple but illustrative models. We initiate the study of the relative frequencies of vacua with vanishing superpotential W=0 and with certain discrete symmetries. For the models we investigate we also compute the overall rate of growth of the number of vacua as a function of the D3-brane charge associated to the fluxes, and the distribution of vacua on the moduli space. The latter two questions can also be addressed by the statistical theory developed by Ashok, Denef and Douglas, and our results are in good agreement with their predictions. Analysis of the first two questions requires methods which are more number-theoretic in nature. We develop some elementary techniques of this type, which are based on arithmetic properties of the periods of the compactification geometry at the points in moduli space where the flux vacua are located.