A T-duality of non-supersymmetric heterotic strings and an implication for Topological Modular Forms

A bstract 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 3 2 ) obtained by fibering the ( E 8 ) 1 × ( E 8 ) 1 current algebra over the two N N = (0, 1) sigma model on S 1 with antiperiodic spin structure (such that the 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 TMF 31 with zero mod-2 elliptic genus.