SO(8) Supergravity and the Magic of Machine Learning

Using de Wit-Nicolai $D=4\;\mathcal{N}=8\;SO(8)$ supergravity as an example, we show how modern Machine Learning software libraries such as Google's TensorFlow can be employed to greatly simplify the analysis of high-dimensional scalar sectors of some M-Theory compactifications. We provide detailed information on the location, symmetries, and particle spectra and charges of 192 critical points on the scalar manifold of SO(8) supergravity, including one newly discovered $\mathcal{N}=1$ vacuum with $SO(3)$ residual symmetry, one new potentially stabilizable non-supersymmetric solution, and examples for "Galois conjugate pairs" of solutions, i.e. solution-pairs that share the same gauge group embedding into~$SO(8)$ and minimal polynomials for the cosmological constant. Where feasible, we give analytic expressions for solution coordinates and cosmological constants. As the authors' aspiration is to present the discussion in a form that is accessible to both the Machine Learning and String Theory communities and allows adopting our methods towards the study of other models, we provide an introductory overview over the relevant Physics as well as Machine Learning concepts. This includes short pedagogical code examples. In particular, we show how to formulate a requirement for residual Supersymmetry as a Machine Learning loss function and effectively guide the numerical search towards supersymmetric critical points. Numerical investigations suggest that there are no further supersymmetric vacua beyond this newly discovered fifth solution.