Bootstrapping Chiral CFTs at Genus Two

TL;DR

This paper develops a method to analyze 2D chiral conformal field theories at genus two by computing conformal blocks and applying bootstrap techniques, leading to bounds on operator data.

Contribution

It introduces an analytical bootstrap approach at genus two using Siegel modular forms, simultaneously enforcing crossing symmetry and modular invariance.

Findings

Derived bounds on three-point functions.

Established constraints on the spectrum of chiral CFTs.

Performed analytical bootstrap at genus two.

Abstract

Genus two partition functions of 2d chiral conformal field theories are given by Siegel modular forms. We compute their conformal blocks and use them to perform the conformal bootstrap. The advantage of this approach is that it imposes crossing symmetry of an infinite family of four point functions and also modular invariance at the same time. Since for a fixed central charge the ring of Siegel modular forms is finite dimensional, we can perform this analytically. In this way we derive bounds on three point functions and on the spectrum of such theories.