STRINGVACUA: A Mathematica Package for Studying Vacuum Configurations in String Phenomenology

TL;DR

STRINGVACUA provides a modular, algebraic-geometry–driven framework for analyzing vacua in string-inspired ${\cal N}=1$ supergravity by recasting extremization conditions as polynomial systems and solving them with Singular via SaturationExpand and Elimination. The workflow—model definition (CreateModel,CalcModel), vacuum-space decomposition, and automated property tests (SturmQuery, stability checks)—is demonstrated on simple and non-perturbative models, with explicit handling of parameter constraints and field-space filtering. The package also generalizes to broad polynomial problems, using DimIdeal, PrimDec, and NumRoots to study solution spaces, counts of real roots, and component structure. Overall, STRINGVACUA offers a practical, extensible tool for exact vacuum analysis in string phenomenology and related polynomial computation tasks, enabling fast, exact insights that were previously hard to obtain.

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.

Figures (8)

• Figure 1: An example of the output of SimpleMinimise.
• Figure 2: An example of a STRINGVACUA protocol notebook.
• Figure 3: An example of the output of SaturationExpand.
• Figure 4: A filtered output from SaturationExpand.
• Figure 5: A example output from SturmQuery.