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A homotopy of 2d SCFTs and an implication for Topological Modular Forms

CMSA EVENTS: CMSA QUANTUM FIELD THEORY AND PHYSICAL MATHEMATICS SEMINAR

When: January 27, 2025
3:00 pm - 4:00 pm
Where: CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138, United States
Speaker: Vivek Saxena (YITP Stony Brook and NHETC Rutgers)

The Segal-Stolz-Teichner conjecture states that there exists an isomorphism between deformation classes of two-dimensional N=(0,1) superconformal field theories (SCFTs) and generalized cohomology classes known as Topological Modular Forms (TMFs). Such 2d N=(0,1) SCFTs arise naturally in physics as worldsheet theories of (possibly compactified) heterotic strings. Recently, this connection was used to prove the absence of global anomalies in heterotic string theories and make predictions about topological terms in their low-energy effective actions, among other things.

In this talk, after giving a brief overview of these ideas, I will describe a physics ”proof” (using methods from 2d CFT) of a mathematical conjecture of Tachikawa and Yamashita about TMF classes in degree 31. Specifically, by examining the two worldsheet theories corresponding to two T-dual nine-dimensional spacetime non-supersymmetric heterotic string theories (namely the $(E_8)_1 \times (E_8)_1$ theory and the $(E_8)_2$ theory), I will argue that the $(E_8)_2$ theory corresponds to the unique nontrivial torsion element $[(E_8)_2]$ of TMF$^{31}$ with zero mod-2 elliptic genus.


In-person and on Zoom

https://harvard.zoom.us/j/97784644596
Password: cmsa