Prof Andre Lukas

Abstract:

We explicitly describe, in the language of four-dimensional N = 1 supersymmetric field theory, what happens when the moduli of a heterotic Calabi-Yau compactification change so as to make the internal non-Abelian gauge fields non-supersymmetric. At the edge of the region in Kähler moduli space where supersymmetry can be preserved, an additional anomalous U (1) gauge symmetry appears in the four-dimensional theory. The D-term contribution to the scalar potential associated to this U (1) attempts to force the system back into a supersymmetric configuration and provides a consistent low-energy description of gauge bundle stability. © 2009 Elsevier B.V. All rights reserved.

Abstract:

We give a simple tutorial introduction to the Mathematica package STRINGVACUA, which is designed to find vacua of string-derived or inspired four-dimensional N = 1 supergravities. The package uses powerful algebro-geometric methods, as implemented in the free computer algebra system Singular, but requires no knowledge of the mathematics upon which it is based. A series of easy-to-use Mathematica modules are provided which can be used both in string theory and in more general applications requiring fast polynomial computations. The use of these modules is illustrated throughout with simple examples. Program summary: Program title: STRINGVACUA. Catalogue identifier: AEBZ_v1_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEBZ_v1_0.html. Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: GNU GPL. No. of lines in distributed program, including test data, etc.: 31 050. No. of bytes in distributed program, including test data, etc.: 163 832. Distribution format: tar.gz. Programming language: "Mathematica" syntax. Computer: Home and office spec desktop and laptop machines, networked or stand alone. Operating system: Windows XP (with Cygwin), Linux, Mac OS, running Mathematica V5 or above. RAM: Varies greatly depending on calculation to be performed. Classification: 11.1. External routines: Linux: The program "Singular" is called from Mathematica. Windows: "Singular" is called within the Cygwin environment from Mathematica. Nature of problem: A central problem of string-phenomenology is to find stable vacua in the four-dimensional effective theories which result from compactification. Solution method: We present an algorithmic method, which uses techniques of algebraic geometry, to find all of the vacua of any given string-phenomenological system in a huge class. Running time: Varies greatly depending on calculation requested. © 2008 Elsevier B.V. All rights reserved.