Vacua of $ω$-deformed SO(8) supergravity

We perform a detailed analysis of the vacua of $ω$-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 $ω$. Apart from describing various properties of different equilibria (390 in total), we show that as $ω$ 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 $ω$-deformation, all of which have guaranteed critical points, and some of which may be novel upliftable solutions.

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