A Comment on Deriving the Gibbons-Hawking-York Term From the String Worldsheet
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917734647857152 |
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| author | Ahmadain, Amr Shyam, Vasudev Yan, Zihan |
| author_facet | Ahmadain, Amr Shyam, Vasudev Yan, Zihan |
| contents | In this note, we show that the noncovariant metric boundary term obtained from the nonlinear sigma model worldsheet derivation of the bulk off-shell sphere partition function is closely related to the Einstein boundary term in the Gamma-Gamma noncovariant action. In fact, when expressed in terms of the trace of the extrinsic curvature tensor, we illustrate that this boundary term has one-half the coefficient of the Gibbons-Hawking-York boundary term required such that the total (bulk plus boundary) off-shell classical action has a well-posed variational principle with Dirichlet boundary conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_18866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Comment on Deriving the Gibbons-Hawking-York Term From the String Worldsheet Ahmadain, Amr Shyam, Vasudev Yan, Zihan High Energy Physics - Theory General Relativity and Quantum Cosmology In this note, we show that the noncovariant metric boundary term obtained from the nonlinear sigma model worldsheet derivation of the bulk off-shell sphere partition function is closely related to the Einstein boundary term in the Gamma-Gamma noncovariant action. In fact, when expressed in terms of the trace of the extrinsic curvature tensor, we illustrate that this boundary term has one-half the coefficient of the Gibbons-Hawking-York boundary term required such that the total (bulk plus boundary) off-shell classical action has a well-posed variational principle with Dirichlet boundary conditions. |
| title | A Comment on Deriving the Gibbons-Hawking-York Term From the String Worldsheet |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2407.18866 |