Gauge Theories, Tessellations & Riemann Surfaces
High Energy Physics - Theory
2015-06-18 v2 Algebraic Geometry
Abstract
We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite graphs on the torus as well as the Platonic and Archimedean solids on the sphere. On higher genus they give rise to intricate patterns. Special attention will be paid to the master space and the moduli space of vacua of the gauge theory and to how their geometry is determined by the tessellations.
Cite
@article{arxiv.1402.3846,
title = {Gauge Theories, Tessellations & Riemann Surfaces},
author = {Yang-Hui He and Mark van Loon},
journal= {arXiv preprint arXiv:1402.3846},
year = {2015}
}
Comments
89 pages, 43 figures; v2: references and comments added, typos fixed