A T-Duality of Non-Supersymmetric Heterotic Strings and an implication for Topological Modular Forms

TL;DR

This paper explores a connection between non-supersymmetric heterotic string theories and Topological Modular Forms, revealing a continuous RG flow linking different theories and providing a physical interpretation of a torsion element in TMF.

Contribution

It demonstrates a novel RG flow connection between specific heterotic string theories and relates this to a torsion element in TMF, bridging string theory and algebraic topology.

Findings

Established a continuous connection between (17,3/2) worldsheet theory and (E8)2 theory.

Linked heterotic string theory to a torsion element in TMF.

Provided a physical derivation of a TMF torsion element via string theory.

Abstract

Motivated by recent developments connecting non-supersymmetric heterotic string theory to the theory of Topological Modular Forms (TMF), we show that the worldsheet theory with central charge $(17,\frac{3}{2})$ obtained by fibering the $(E_8)_1 \times (E_8)_1$ current algebra over the $\mathit{N}$=(0,1) sigma model on $S^{1}$ with antiperiodic spin structure (such that the two $E_8$ factors are exchanged as we go around the circle), is continuously connected to the $(E_8)_2$ theory in the Gaiotto$-$Johnson-Freyd$-$Witten sense of going "up and down the RG trajectories". Combined with the work of Tachikawa and Yamashita, this furnishes a physical derivation of the fact that the $(E_8)_2$ theory corresponds to the unique nontrivial torsion element $[(E_8)_2]$ of $\mathsf{TMF}^{31}$ with zero mod-2 elliptic genus.