Numerical Analyses on Moduli Space of Vacua
arXiv:1210.6038 · doi:10.1007/JHEP09(2013)083
Abstract
We propose a new computational method to understand the vacuum moduli space of (supersymmetric) field theories. By combining numerical algebraic geometry (NAG) and elimination theory, we develop a powerful, efficient, and parallelizable algorithm to extract important information such as the dimension, branch structure, Hilbert series and subsequent operator counting, as well as variation according to coupling constants and mass parameters. We illustrate this method on a host of examples from gauge theory, string theory, and algebraic geometry.
31 pages, 3 figures. Results for bigger systems included and references updated
References in corpus (7)
- SQCD: A Geometric Apercu
- Heterotic Compactification, An Algorithmic Approach
- STRINGVACUA: A Mathematica Package for Studying Vacuum Configurations in String Phenomenology
- Hilbert Series for Flavor Invariants of the Standard Model
- Exploring the Vacuum Geometry of N=1 Gauge Theories
- Finding all flux vacua in an explicit example
- Enumerating Gribov copies on the lattice
Cited by in corpus (8)
- Finding all flux vacua in an explicit example
- Global Structure of Curves from Generalized Unitarity Cut of Three-loop Diagrams
- Enumerating Copies in the First Gribov Region on the Lattice in up to four Dimensions
- Veronese Geometry and the Electroweak Vacuum Moduli Space
- Gauge Theories, Tessellations & Riemann Surfaces
- Gauge-fixing on the Lattice via Orbifolding
- Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases
- The Statistics of Vacuum Geometry