Properties of the wormhole-dominant phase in two-dimensional quantum gravity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912403034210304 |
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| author | Kuroki, Tsunehide Sato, Yuki |
| author_facet | Kuroki, Tsunehide Sato, Yuki |
| contents | We study the $N \times N$ Hermitian one-matrix model modified by the double-trace interaction. It is known that the coupling for the double-trace interaction can control the weight for the microscopic wormholes if interpreting the matrix model as the lattice model of random surface; tuning the coupling to its critical value, the effect of wormholes become substantial to change the critical behavior of the pure $2$D quantum gravity, which is characterized by a certain positive value of the string susceptibility. In the large-$N$ limit, we calculate the continuum limit of the disk amplitude in which the wormhole effects are important. The resulting continuum disk amplitude is the same as that of the pure $2$D quantum gravity. We also introduce the renormalized coupling for the double-trace interaction, and show that the newly introduced renormalized coupling can alter the renormalized bulk cosmological constant effectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_00369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Properties of the wormhole-dominant phase in two-dimensional quantum gravity Kuroki, Tsunehide Sato, Yuki High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Lattice We study the $N \times N$ Hermitian one-matrix model modified by the double-trace interaction. It is known that the coupling for the double-trace interaction can control the weight for the microscopic wormholes if interpreting the matrix model as the lattice model of random surface; tuning the coupling to its critical value, the effect of wormholes become substantial to change the critical behavior of the pure $2$D quantum gravity, which is characterized by a certain positive value of the string susceptibility. In the large-$N$ limit, we calculate the continuum limit of the disk amplitude in which the wormhole effects are important. The resulting continuum disk amplitude is the same as that of the pure $2$D quantum gravity. We also introduce the renormalized coupling for the double-trace interaction, and show that the newly introduced renormalized coupling can alter the renormalized bulk cosmological constant effectively. |
| title | Properties of the wormhole-dominant phase in two-dimensional quantum gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2501.00369 |