The many vacua of gauged extended supergravities

A novel method is presented which employs advanced numerical techniquesused in the engineering sciences to find and study the properties of nontrivialvacua of gauged extended supergravity models. While this method only producesapproximate numerical data rather than analytic results, it overcomes the previouslimitation of only being able to find vacua with large residual unbroken gauge symmetrygroups. The effectiveness of this method is demonstrated by applying it to thetechnically most challenging D ? 3 scalar potential—that of SO(8) × SO(8) gaugedN = 16 Chern–Simons Supergravity in D = 3. Extensive data on the properties of99 different vacua (92 of them new) of this model are given. Furthermore, techniquesare briefly discussed which should allow using this numerical information as an inputto the construction of semi-automatic stringent analytic proofs on the locations andproperties of vacua. It hence is argued that these combined techniques presumably arepowerful enough to systematically map all the nontrivial vacua of every supergravitymodel