Numerical tools to validate stationary points of [formula omitted]-gauged [formula omitted][formula omitted] supergravity

Abstract

Until recently, the preferred strategy to identify stationary points in the scalar potential of SO ( 8 ) -gauged N = 8 supergravity in D = 4 has been to consider truncations of the potential to sub-manifolds of E 7 ( + 7 ) / SU ( 8 ) that are invariant under some postulated residual gauge group 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 ) 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 summary Program title: e7-vacua Catalogue identifier: AELB_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AELB_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4447 No. of bytes in distributed program, including test data, etc.: 281 689 Distribution format: tar.gz Programming language: Python Computer: Any Operating system: Unix/Linux RAM: 1 Giga-byte Classification: 1.5, 11.1 External 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 ) -gauged N = 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.