From Binary Error Correcting Codes to a Relation Between Maximal D=4 and D=3 Supergravities

TL;DR

This paper provides numerical evidence for the embedding of scalar potentials from four-dimensional N=8 supergravity into three-dimensional N=16 supergravity, revealing a relation between different supergravity theories.

Contribution

It demonstrates, using TensorFlow-based numerical methods, the embedding of scalar potentials between supergravity theories and identifies the role of the dyonic omega-angle in this embedding.

Findings

Numerical evidence supports the embedding of scalar potentials in the limit of a scalar parameter.

The dyonic omega-angle corresponds to the U(1) part of the SL(2) factor.

The embedding relates maximal supergravities in different dimensions.

Abstract

This short note provides (TensorFlow-based) numerical evidence for the embedability (in the limit of a scalar parameter going to infinity) of the scalar potential of dyonic N=8, D=4 SO(8) supergravity into the scalar potential of N=16, D=3 SO(8)xSO(8) supergravity. One finds that the dyonic $\omega$-angle gets identified with the compact U(1) part of the SL(2) factor of the SL(2)xE7(7) subgroup of E8(8).