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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, 32) obtained by fibering the (E₈) ₁ (E₈) ₁ current algebra over the N= (0, 1) sigma model on S^1 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 TMF^31 with zero mod-2 elliptic genus.
Vivek Saxena (Wed,) studied this question.