The many vacua of gauged extended supergravities

TL;DR

This paper introduces a new numerical method to identify and analyze nontrivial vacua in gauged extended supergravity models, overcoming previous limitations and providing extensive data on numerous vacua, including many new ones.

Contribution

A novel numerical approach is developed to find and study vacua in supergravity models, enabling analysis of vacua with minimal residual symmetry and extensive data collection.

Findings

Identified 99 vacua in SO(8) x SO(8) gauged supergravity, 92 of which are new.

Demonstrated the method's effectiveness on complex scalar potentials in supergravity.

Provided data and techniques to aid in constructing analytic proofs of vacua properties.

Abstract

A novel method is presented which employs advanced numerical techniques used in the engineering sciences to find and study the properties of nontrivial vacua of gauged extended supergravity models. While this method only produces approximate numerical data rather than analytic results, it overcomes the previous limitation of only being able to find vacua with large residual unbroken gauge symmetry groups. The effectiveness of this method is demonstrated by applying it to the technically most challenging D>=3 scalar potential -- that of SO(8) X SO(8) gauged N=16 Chern-Simons Supergravity in D=3. Extensive data on the properties of 99 different vacua (92 of them new) of this model are given. Furthermore, techniques are briefly discussed which should allow using this numerical information as an input to the construction of semi-automatic stringent analytic proofs on the locations and properties of vacua. It hence is argued that these combined techniques presumably are powerful enough to systematically map all the nontrivial vacua of every supergravity model.