Abstract
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.
Highlights
Introduction1Google’s primary open source library for Machine Learning, TensorFlow [2], has many potential uses beyond Machine Learning
At the moment, the N = 8 Supergravity Theory is the only candidate in sight
If supersymmetry [10] is part of the answer why the observed fundamental laws of physics are the way they are, due to the existence of gravity, there is no way to escape the conclusion that a viable theory must contain supergravity [11, 12] and in particular a supersymmetric
Summary
Google’s primary open source library for Machine Learning, TensorFlow [2], has many potential uses beyond Machine Learning. Despite the remarkable success of the Standard Model (SM) of Elementary Particle Physics [18], which quantitatively describes the properties and interactions of matter and force particles so well that the LHC at the time of this writing did not to come up with clear evidence of “new” (beyond-the-SM) physics, there are a number of unsolved problems, for example non-observation of the particles that constitute Dark Matter [19], or explaining why the neutron’s electric dipole moment is too small to be measurable [20] The most puzzling such problem of theoretical physics currently is perhaps explaining the observed positive — but from a quantum field theory perspective extremely small — vacuum energy density [21] of the universe. Even if M-Theory turned out to not be the correct answer to the question how to quantize gravity, it already has made major contributions to uncovering interesting hidden connections in pure mathematics, of which we here only want to mention the geometric Langlands correspondence as one example, [22]
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