Triality, Periodicity and Stability of SO(8) Gauged Supergravity

TL;DR

This paper investigates the periodicity and stability of SO(8) gauged supergravity solutions, revealing a triality-related three-branch structure with a Pi/4 periodicity in the vacuum landscape.

Contribution

It classifies critical points in SO(4) invariant sectors, introduces a new non-supersymmetric unstable branch, and links triality to solution periodicity.

Findings

Discovery of a novel non-supersymmetric unstable solution branch.

Identification of a Pi/4 periodicity in the vacuum structure.

Analysis of triality's role in the interrelation of solutions.

Abstract

While electromagnetic duality is a symmetry of many supergravity theories, this is not the case for the N=8 gauged theory. It was recently shown that this rotation leads to a one-parameter family of SO(8) supergravities. It is an open question what the period of this parameter is. This issue is investigated in the SO(4) invariant sectors of the theory. We classify such critical points and find a novel branch of non-supersymmetric and unstable solutions, whose embedding is related via triality to the two known ones. Secondly, we show that the three branches of solutions lead to a Pi/4 periodicity of the vacuum structure. The general interrelations between triality and periodicity are discussed. Finally, we comment on the connection to other gauge groups as well as the possibility to achieve (non-)perturbative stability around AdS/Mkw/dS transitions.