Genus 2 Superstring Chiral Measure From The 3-Dimensional Gelca-Hamilton TQFT
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917970707480576 |
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| author | Koizumi, Saki |
| author_facet | Koizumi, Saki |
| contents | In the path integral formulation of the superstring, the chiral measure acquires a phase under the modular transformation of a Riemann surface. This motivated the use of anomaly inflow to define the superstring chiral measure by a path integral formalism of a modular invariant $3$-dimensional theory. A Gelca-Hamilton topological field theory (TQFT) is one of the Atiyah's TQFT on a $3$-dimensional extended manifold with the boundary Jacobi variety of a Riemann surface, whose Hilbert space is spanned by the theta series. We show that genus $g\leq 2$ superstring chiral measure in the path integral can be obtained by the path integral of the Gelca-Hamilton TQFT on some $3$-dimensional bulk extended manifolds. The modular transformation of the superstring chiral measure can be understood as the action of the extended mapping class group on the bulk $3$-dimensional extended manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19342 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Genus 2 Superstring Chiral Measure From The 3-Dimensional Gelca-Hamilton TQFT Koizumi, Saki High Energy Physics - Theory In the path integral formulation of the superstring, the chiral measure acquires a phase under the modular transformation of a Riemann surface. This motivated the use of anomaly inflow to define the superstring chiral measure by a path integral formalism of a modular invariant $3$-dimensional theory. A Gelca-Hamilton topological field theory (TQFT) is one of the Atiyah's TQFT on a $3$-dimensional extended manifold with the boundary Jacobi variety of a Riemann surface, whose Hilbert space is spanned by the theta series. We show that genus $g\leq 2$ superstring chiral measure in the path integral can be obtained by the path integral of the Gelca-Hamilton TQFT on some $3$-dimensional bulk extended manifolds. The modular transformation of the superstring chiral measure can be understood as the action of the extended mapping class group on the bulk $3$-dimensional extended manifolds. |
| title | Genus 2 Superstring Chiral Measure From The 3-Dimensional Gelca-Hamilton TQFT |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.19342 |