A T-Duality of Non-Supersymmetric Heterotic Strings and an implication for Topological Modular Forms
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916392369913856 |
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| author | Saxena, Vivek |
| author_facet | Saxena, Vivek |
| contents | 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 $\mathit{N}$=(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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19409 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A T-Duality of Non-Supersymmetric Heterotic Strings and an implication for Topological Modular Forms Saxena, Vivek High Energy Physics - Theory Mathematical Physics Algebraic Topology 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 $\mathit{N}$=(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. |
| title | A T-Duality of Non-Supersymmetric Heterotic Strings and an implication for Topological Modular Forms |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Topology |
| url | https://arxiv.org/abs/2405.19409 |