Holomorphic CFTs and Topological Modular Forms

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 super symmetric 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.

Automated summary

We use the theory of topological modular forms to restrict bosonic holomorphic CFTs, which can be seen as (0, 1) SCFTs with trivial right-moving super symmetric 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 confirm this constraint in large classes of physical examples and disprove the existence of an infinite set of extremal CFTs, including those with central charges c = 48, 72, 96, and 120.