Vacua of $\omega$-deformed SO(8) supergravity

TL;DR

This paper analyzes how vacua of $$ supergravity change with the electric-magnetic deformation parameter $$, revealing new critical points and connections to known supergravity solutions using numerical methods.

Contribution

It introduces a numerical approach to track vacua in $$ supergravity as the deformation parameter varies, identifying new critical points and their upliftability.

Findings

390 vacua analyzed in detail

Deformation relates a known vacuum to a critical point in another supergravity theory

Method enables discovery of new admissible gaugings with guaranteed critical points

Abstract

We perform a detailed analysis of the vacua of $\omega$-deformed SO(8) supergravity in four dimensions. In particular, using Tensorflow-based numerical methods, we track how the equilibria of the theory change when varying the electric-magnetic deformation parameter $\omega$. Apart from describing various properties of different equilibria (390 in total), we show that as $\omega$ is deformed, the SO(3), N=1 vacuum of the de Wit-Nicolai theory becomes equivalent to a critical point in $U(4)\ltimes\mathbb{R}^{12}$ gauged supergravity with a known uplift in IIB supergravity. The procedure employed here to obtain a new gauging with a guaranteed equilibrium is generic and allows one to obtain further admissible noncompact gaugings via $\omega$-deformation, all of which have guaranteed critical points, and some of which may be novel upliftable solutions.