Four-point correlation numbers in super Minimal Liouville Gravity in the Ramond sector
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| Format: | Preprint |
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2026
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| author | Belavin, Vladimir Cabezas, Juan Ramos Runov, Boris |
| author_facet | Belavin, Vladimir Cabezas, Juan Ramos Runov, Boris |
| contents | In this work, we continue the investigation of correlation numbers in $\mathcal{N}=1$ super Minimal Liouville Gravity (SMLG), with physical fields in the Ramond sector. Building upon our previous construction of physical operators and the evaluation of three-point correlation functions involving Ramond and Neveu-Schwarz (NS) insertions, we now turn to the analytic computation of four-point correlation numbers. This development is motivated by the framework established for the bosonic Minimal Liouville Gravity and its supersymmetric NS analog, where the integration over moduli space in correlation functions can be performed explicitly using the higher equations of motion (HEM) in Liouville theory. In particular, if one of the insertions corresponds to a degenerate field, the four-point amplitude can be expressed in terms of boundary contributions obtained from the OPE structure of logarithmic counterparts of ground ring elements. We aim to adapt and generalize this approach to the Ramond sector.Our result is a closed-form analytic expression for four-point correlation numbers involving Ramond fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_24354 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Four-point correlation numbers in super Minimal Liouville Gravity in the Ramond sector Belavin, Vladimir Cabezas, Juan Ramos Runov, Boris High Energy Physics - Theory Mathematical Physics In this work, we continue the investigation of correlation numbers in $\mathcal{N}=1$ super Minimal Liouville Gravity (SMLG), with physical fields in the Ramond sector. Building upon our previous construction of physical operators and the evaluation of three-point correlation functions involving Ramond and Neveu-Schwarz (NS) insertions, we now turn to the analytic computation of four-point correlation numbers. This development is motivated by the framework established for the bosonic Minimal Liouville Gravity and its supersymmetric NS analog, where the integration over moduli space in correlation functions can be performed explicitly using the higher equations of motion (HEM) in Liouville theory. In particular, if one of the insertions corresponds to a degenerate field, the four-point amplitude can be expressed in terms of boundary contributions obtained from the OPE structure of logarithmic counterparts of ground ring elements. We aim to adapt and generalize this approach to the Ramond sector.Our result is a closed-form analytic expression for four-point correlation numbers involving Ramond fields. |
| title | Four-point correlation numbers in super Minimal Liouville Gravity in the Ramond sector |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2603.24354 |