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

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 (17,3/2) obtained by fibering the (E₈)₁ × (E₈)₁ current algebra over the N=(0,1) sigma model on S¹ with antiperiodic spin structure (such that the two E₈ factors are exchanged as we go around the circle), is continuously connected to the (E₈)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 (E₈)₂ theory corresponds to the unique nontrivial torsion element [(E₈)₂] of TMF³¹ with zero mod-2 elliptic genus.