Events Daily

Tuesday, August 30, 2022

Topological modular forms and Monstrous Moonshine
Ying-Hsuan Lin, Harvard University
Event Type: Informal HEP Talk
Time: 11:00 AM - 12:30 PM
Location: 726 Broadway, 940, CCPP Seminar
Abstract: We use the theory of topological modular forms to constrain bosonic holomorphic CFTs, which can be viewed as (0,1) SCFTs with a 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. Applying the constraint to orbifolds of multiple copies of the Monster CFT, and aided by Borcherds' generalized denominator formula, we are further led to number-theoretic observations on the Fourier coefficients of the McKay-Thompson series.