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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2509.17973 |
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| _version_ | 1866914339401760768 |
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| author | Arrighi, Federico Khandelwal, Saurish Lechtenfeld, Olaf |
| author_facet | Arrighi, Federico Khandelwal, Saurish Lechtenfeld, Olaf |
| contents | We investigate the possibility of a Nicolai map for minimal supergravity in four dimensions. Such a map would allow for the computation of quantum supergravity correlation functions in terms of flat-space correlators in an effective nonlocal bosonic theory with the help of a nonlinear field transformation, the inverse Nicolai map. Such a map is guaranteed for off-shell global supersymmetry, but local supersymmetry presents at least three obstacles for the construction. Their effects are analyzed in detail, in an attempt to set up a Nicolai map to leading order in the gravitational coupling. We find indications that the conformal factor of the metric obstructs the off-shell construction, suggesting that the unimodular variant of supergravity may do better. The on-shell supersymmetry approach, successful for super-Yang-Mills theory in its critical dimensions, also fails, because the graviton self-interaction cannot be written as a supervariation. Nevertheless, by brute force we obtain a four-parameter first-order Nicolai map fulfilling the free-action condition. For the acid test of determinant matching, however, one needs to push the general ansatz and the perturbative expansion to the second order and to the quantum level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17973 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards a Nicolai map for supergravity Arrighi, Federico Khandelwal, Saurish Lechtenfeld, Olaf High Energy Physics - Theory We investigate the possibility of a Nicolai map for minimal supergravity in four dimensions. Such a map would allow for the computation of quantum supergravity correlation functions in terms of flat-space correlators in an effective nonlocal bosonic theory with the help of a nonlinear field transformation, the inverse Nicolai map. Such a map is guaranteed for off-shell global supersymmetry, but local supersymmetry presents at least three obstacles for the construction. Their effects are analyzed in detail, in an attempt to set up a Nicolai map to leading order in the gravitational coupling. We find indications that the conformal factor of the metric obstructs the off-shell construction, suggesting that the unimodular variant of supergravity may do better. The on-shell supersymmetry approach, successful for super-Yang-Mills theory in its critical dimensions, also fails, because the graviton self-interaction cannot be written as a supervariation. Nevertheless, by brute force we obtain a four-parameter first-order Nicolai map fulfilling the free-action condition. For the acid test of determinant matching, however, one needs to push the general ansatz and the perturbative expansion to the second order and to the quantum level. |
| title | Towards a Nicolai map for supergravity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.17973 |