1:30 pm MCP 201
A homotopy of 2d SQFTs and Topological Modular Forms.
The Segal-Stolz-Teichner conjecture asserts the existence of an isomorphism between deformation classes of two-dimensional N = (0, 1) supersymmetric quantum field theories (SQFTs) and generalized cohomology classes known as Topological Modular Forms (TMFs). A subclass of such theories is given by two-dimensional N = (0, 1) superconformal field theories (SCFTs) which arise as worldsheet theories of (possibly compactified) heterotic strings. TMF classes measure subtle torsion invariants and have played an important role in proving the absence of global anomalies in heterotic string theories and making predictions about topological terms in their low-energy effective actions.
In this talk, after giving a brief pedagogical overview of TMF, I will describe a physics “proof” (using ideas from 2d CFT) of a mathematical conjecture about TMF classes in degree 31 which correspond to worldsheet SCFTs of two nine-dimensional spacetime non-supersymmetric heterotic string theories, namely the (E8)1 × (E8)1 theory and the (E8)2 theory. Specifically, I will argue that these theories are continuously connected (“homotopic”) in the space of theories, and that the (E8)2 theory corresponds to the unique nontrivial torsion element [(E8)2] of TMF31 with zero mod-2 elliptic genus.