Numerical tools to validate stationary points of SO(8)-gauged N=8 D=4 supergravity
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 E7(+7)/SU(8) that are invariant under some postulated residual gauge group G subset of 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, Queen's 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. (C) 2011 Elsevier B.V. All rights reserved.
stationary points potential critical points maximal gauged supergravity spontaneous symmetry breaking vacua