Conformal field theories and compact curves in moduli spaces

TL;DR

This paper explores the structure of the moduli space of Riemann surfaces, revealing many compact subsets avoiding symmetry loci, with implications for supersymmetric conformal field theories in four dimensions.

Contribution

It demonstrates the existence of numerous compact subsets in the moduli space that do not intersect symmetry loci, linking geometric properties to physical theories.

Findings

Many compact subsets of the moduli space avoid symmetry loci

Implications for $ abla=2$ supersymmetric conformal field theories in 4D

New insights into the geometry of Riemann surface moduli spaces

Abstract

We show that there are many compact subsets of the moduli space $M_g$ of Riemann surfaces of genus $g$ that do not intersect any symmetry locus. This has interesting implications for $\mathcal{N}=2$ supersymmetric conformal field theories in four dimensions.