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

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 $N$=(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.

26 pages + appendices; References updated; Content matches published version

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