On the vacua of N = 8 gauged supergravity in 4 dimensions

TL;DR

The paper introduces a new method for finding vacua in N=8 gauged supergravity in 4D by varying the embedding tensor, successfully recovering known vacua and discovering new solutions, with insights into moduli spaces and cosmological constants.

Contribution

A novel procedure based on the embedding tensor variation for identifying vacua in N=8 gauged supergravity, enabling the discovery of new solutions and analysis of moduli space structure.

Findings

Recovered many known vacua and completed their scalar mass spectra.

Discovered a dozen new analytical vacuum solutions.

Provided criteria for the cosmological constant based on group properties.

Abstract

We discuss a simple procedure for finding vacua of gauged supergravity models, based on the variation of the embedding tensor rather than on a direct minimization of the scalar potential. We apply this procedure to N=8 gauged supergravity in 4 dimensions. We easily recover many of the previously known vacua, also completing their scalar mass spectrum, and we apply our procedure to find a dozen of new analytical vacuum solutions. The analysis shows an interesting structure on the moduli spaces of these vacua and provides new criteria to determine the expected value of the cosmological constant by a simple inspection of the group properties of the embedding tensor.