Holomorphic CFTs and topological modular forms

TL;DR

This paper applies topological modular forms to constrain bosonic holomorphic conformal field theories, verifying conjectured divisibility conditions and ruling out certain extremal theories with specific central charges.

Contribution

It introduces a novel use of topological modular forms to impose constraints on holomorphic CFTs and verifies these constraints in various examples.

Findings

Constant term of partition function divisible by specific integers

Ruling out infinite sets of extremal CFTs with certain central charges

Verification of Segal-Stolz-Teichner conjecture in physical examples

Abstract

We use the theory of topological modular forms to constrain bosonic holomorphic CFTs, which can be viewed as $(0,1)$ SCFTs with trivial right-moving supersymmetric sector. A conjecture by Segal, Stolz and Teichner requires the constant term of the partition function to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of extremal CFTs, including those with central charges $c=48, 72, 96$ and $120$.