Gravitational index of the heterotic string
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866907908303749120 |
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| author | Chen, Yiming Murthy, Sameer Turiaci, Gustavo J. |
| author_facet | Chen, Yiming Murthy, Sameer Turiaci, Gustavo J. |
| contents | The fundamental heterotic string has a tower of BPS states whose supersymmetric index has an exponential growth in the charges. We construct the saddle-point of the gravitational path integral corresponding to this index. The saddle-point configuration is a supersymmetric rotating non-extremal Euclidean black hole. This configuration is singular in the two-derivative theory. We show that the addition of higher-derivative terms in four-dimensional $N=2$ supergravity resolves the singularity. In doing so, we extend the recently-developed "new attractor mechanism" to include the effect of higher-derivative terms. Remarkably, the one-loop, four-derivative F-term contribution to the prepotential leads to a precise match of the gravitational and microscopic index. We also comment, using the effective theory near the horizon, on the possibility of a string-size near-extremal black hole. Our results clarify the meaning of different descriptions of this system in the literature. The thermal state transitions to a winding condensate and a gas of strings without ever reaching a small black hole, while the index is captured by the rotating Euclidean black hole solution and is constant and thus smoothly connected to the microscopic ensemble. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_03297 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gravitational index of the heterotic string Chen, Yiming Murthy, Sameer Turiaci, Gustavo J. High Energy Physics - Theory General Relativity and Quantum Cosmology The fundamental heterotic string has a tower of BPS states whose supersymmetric index has an exponential growth in the charges. We construct the saddle-point of the gravitational path integral corresponding to this index. The saddle-point configuration is a supersymmetric rotating non-extremal Euclidean black hole. This configuration is singular in the two-derivative theory. We show that the addition of higher-derivative terms in four-dimensional $N=2$ supergravity resolves the singularity. In doing so, we extend the recently-developed "new attractor mechanism" to include the effect of higher-derivative terms. Remarkably, the one-loop, four-derivative F-term contribution to the prepotential leads to a precise match of the gravitational and microscopic index. We also comment, using the effective theory near the horizon, on the possibility of a string-size near-extremal black hole. Our results clarify the meaning of different descriptions of this system in the literature. The thermal state transitions to a winding condensate and a gas of strings without ever reaching a small black hole, while the index is captured by the rotating Euclidean black hole solution and is constant and thus smoothly connected to the microscopic ensemble. |
| title | Gravitational index of the heterotic string |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2402.03297 |