Rigorous results for timelike Liouville field theory
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909013800648704 |
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| author | Chatterjee, Sourav |
| author_facet | Chatterjee, Sourav |
| contents | Liouville field theory has long been a cornerstone of two-dimensional quantum field theory and quantum gravity, which has attracted much recent attention in the mathematics literature. Timelike Liouville field theory is a version of Liouville field theory where the kinetic term in the action appears with a negative sign, which makes it closer to a theory of quantum gravity than ordinary (spacelike) Liouville field theory. Making sense of this `wrong sign' requires a theory of Gaussian random variables with negative variance. Such a theory is developed in this paper, and is used to prove the timelike DOZZ formula for the $3$-point correlation function when the parameters satisfy the so-called `charge neutrality condition'. Expressions are derived also for the $k$-point correlation functions for all $k\ge 3$, and it is shown that these functions approach the correct semiclassical limits as the coupling constant is sent to zero |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02348 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigorous results for timelike Liouville field theory Chatterjee, Sourav Probability High Energy Physics - Theory Mathematical Physics 81T40, 17B69, 81T20 Liouville field theory has long been a cornerstone of two-dimensional quantum field theory and quantum gravity, which has attracted much recent attention in the mathematics literature. Timelike Liouville field theory is a version of Liouville field theory where the kinetic term in the action appears with a negative sign, which makes it closer to a theory of quantum gravity than ordinary (spacelike) Liouville field theory. Making sense of this `wrong sign' requires a theory of Gaussian random variables with negative variance. Such a theory is developed in this paper, and is used to prove the timelike DOZZ formula for the $3$-point correlation function when the parameters satisfy the so-called `charge neutrality condition'. Expressions are derived also for the $k$-point correlation functions for all $k\ge 3$, and it is shown that these functions approach the correct semiclassical limits as the coupling constant is sent to zero |
| title | Rigorous results for timelike Liouville field theory |
| topic | Probability High Energy Physics - Theory Mathematical Physics 81T40, 17B69, 81T20 |
| url | https://arxiv.org/abs/2504.02348 |