On a long exact sequence of groups of equivalence classes of 2d $\mathcal{N}{=}(0,1)$ SQFTs
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912588727582720 |
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| author | Tachikawa, Yuji |
| author_facet | Tachikawa, Yuji |
| contents | Strongly motivated by a mathematical result by Lin and Yamashita (arXiv:2412.02298), we describe a long exact sequence formed by groups of equivalence classes of two-dimensional $\mathcal{N}{=}(0,1)$ supersymmetric quantum field theories (SQFTs) with and without $SU(2)$ symmetry. As an application, we study chiral fermions in heterotic compactifications with $SU(2)$ symmetry of level one to four dimensions, and show that each even-dimensional irreducible representation of $SU(2)$ appears even times, assuming the conjectural relation between topological modular forms and SQFTs. This implies the absence of the Witten anomaly, but contains more information than that. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12481 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a long exact sequence of groups of equivalence classes of 2d $\mathcal{N}{=}(0,1)$ SQFTs Tachikawa, Yuji High Energy Physics - Theory Strongly motivated by a mathematical result by Lin and Yamashita (arXiv:2412.02298), we describe a long exact sequence formed by groups of equivalence classes of two-dimensional $\mathcal{N}{=}(0,1)$ supersymmetric quantum field theories (SQFTs) with and without $SU(2)$ symmetry. As an application, we study chiral fermions in heterotic compactifications with $SU(2)$ symmetry of level one to four dimensions, and show that each even-dimensional irreducible representation of $SU(2)$ appears even times, assuming the conjectural relation between topological modular forms and SQFTs. This implies the absence of the Witten anomaly, but contains more information than that. |
| title | On a long exact sequence of groups of equivalence classes of 2d $\mathcal{N}{=}(0,1)$ SQFTs |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.12481 |