The Statistics of Vacuum Geometry

Abstract

We investigate the vacuum moduli space of supersymmetric gauge theories en masse by probing the space of such vacua from a statistical standpoint. Using quiver gauge theories with $\mathcal{N}=1$ supersymmetry as a testing ground, we sample over a large number of vacua as algebraic varieties, computing explicitly their dimension, degree and Hilbert series. We study the distribution of these geometrical quantities, and also address the question of how likely it is for the moduli space to be Calabi-Yau.

34 pages, 13 tables, 6 figures

References in corpus (6)

• The Master Space of N=1 Gauge Theories
• SQCD: A Geometric Apercu
• STRINGVACUA: A Mathematica Package for Studying Vacuum Configurations in String Phenomenology
• Hilbert Series for Flavor Invariants of the Standard Model
• Classification of 4d N=2 gauge theories
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Cited by in corpus (1)

• Analyzing Multi-Field Tunneling With Exact Bounce Solutions