Localization of strings on group manifolds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911172812341248 |
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| author | Murthy, Sameer Witten, Edward |
| author_facet | Murthy, Sameer Witten, Edward |
| contents | We compute the partition function of the WZW model with target a compact Lie group $G$ by adapting a method used by Choi and Takhtajan to compute the heat kernel of the group manifold. The basic idea is to compute the partition function of a supersymmetric version of the WZW model using a form of supersymmetric localization and then use the fact that, since the fermions of the supersymmetric WZW model are actually decoupled from the bosons, this also determines the partition function of the purely bosonic WZW model. The result is a formula for the partition function as a sum over contributions from abelian classical solutions. We verify for $G=SU(2)$ that this formula agrees with the result for the same partition function that comes from the Weyl-Kac character formula. We extend the method of supersymmetric localization to certain related models such as the $SL(2,\mathbb{R})$ WZW model and a Wick-rotated version of this model in which the target space is hyperbolic three-space $H_3^+$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localization of strings on group manifolds Murthy, Sameer Witten, Edward High Energy Physics - Theory Number Theory Representation Theory We compute the partition function of the WZW model with target a compact Lie group $G$ by adapting a method used by Choi and Takhtajan to compute the heat kernel of the group manifold. The basic idea is to compute the partition function of a supersymmetric version of the WZW model using a form of supersymmetric localization and then use the fact that, since the fermions of the supersymmetric WZW model are actually decoupled from the bosons, this also determines the partition function of the purely bosonic WZW model. The result is a formula for the partition function as a sum over contributions from abelian classical solutions. We verify for $G=SU(2)$ that this formula agrees with the result for the same partition function that comes from the Weyl-Kac character formula. We extend the method of supersymmetric localization to certain related models such as the $SL(2,\mathbb{R})$ WZW model and a Wick-rotated version of this model in which the target space is hyperbolic three-space $H_3^+$. |
| title | Localization of strings on group manifolds |
| topic | High Energy Physics - Theory Number Theory Representation Theory |
| url | https://arxiv.org/abs/2506.20028 |