Abstract
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,$$ \frac{3}{2} $$
3
2
) obtained by fibering the (E8)1 × (E8)1 current algebra over the two $$ \mathcal{N} $$
N
= (0, 1) sigma model on S1 with antiperiodic spin structure (such that the 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.
Publisher
Springer Science and Business Media LLC
Reference88 articles.
1. D. Gaiotto, T. Johnson-Freyd and E. Witten, A Note On Some Minimally Supersymmetric Models In Two Dimensions, arXiv:1902.10249 [INSPIRE].
2. M.J. Hopkins, Topological Modular Forms, the Witten Genus, and the Theorem of the Cube, in Proceedings of the International Congress of Mathematicians, S.D. Chatterji ed., Birkhäuser Basel, (1995), p. 554–565 [https://doi.org/10.1007/978-3-0348-9078-6_49].
3. M.J. Hopkins, Algebraic topology and modular forms, math/0212397.
4. M.J. Hopkins and I.M. Singer, Quadratic functions in geometry, topology, and M theory, J. Diff. Geom. 70 (2005) 329 [math/0211216] [INSPIRE].
5. P.G. Goerss, Topological modular forms (aftern Hopkins, Miller, and Lurie), arXiv:0910.5130.