Prof Andre Lukas

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.

Abstract:

We explicitly construct the largest dataset to date of heterotic vacua arising from stable vector bundles on Calabi-Yau threefolds. Focusing on elliptically fibered Calabi-Yau manifolds with spectral cover bundles, we show that the number of heterotic models with non-zero number of generations is finite. We classify these models according to the complex base of their Calabi-Yau threefold and to the unification gauge group that they preserve in four dimensions. This database of the order of 107 models, which includes potential Standard Model candidates, is subjected to some preliminary statistical analyses. The additional constraint that there should be three net generations of particles gives a dramatic reduction of the number of vacua. © 2008 SISSA.