Numerical tools to validate stationary points of SO(8)SO(8)-gauged N=8N=8D=4D=4 supergravity

Until recently, the preferred strategy to identify stationary points in the scalar potential of SO(8)SO(8)-gauged N=8N=8 supergravity in D=4D=4 has been to consider truncations of the potential to sub-manifolds of E7(+7)/SU(8)E7(+7)/SU(8) that are invariant under some postulated residual gauge group G⊂SO(8)G⊂SO(8). As powerful alternative strategies have been shown to exist that allow one to go far beyond what this method can achieve — and in particular have produced numerous solutions that break the SO(8)SO(8) gauge group to no continuous residual symmetry — independent verification of results becomes a problem due to both the complexity of the scalar potential and the large number of new solutions. This article introduces a conceptually simple self-contained piece of computer code that allows independent numerical validation of claims on the locations of newly discovered stationary points.Program summaryProgram title: e7-vacuaCatalogue identifier: AELB_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELB_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 4447No. of bytes in distributed program, including test data, etc.: 281 689Distribution format: tar.gzProgramming language: PythonComputer: AnyOperating system: Unix/LinuxRAM: 1 Giga-byteClassification: 1.5, 11.1External routines: Scientific Python (SciPy) (http://www.scipy.org/), NumPy (http://numpy.scipy.org)Nature of problem:   This code allows numerical validation of claims about the existence of critical points in the scalar potential of four-dimensional SO(8)SO(8)-gauged N=8N=8 supergravity.Solution method: Tensor algebra.Running time: Full analysis of a solution (including scalar mass matrices): about 15 minutes. Otherwise, about 1–2 minutes.