The coupling flow for supergravity
- 1Leibniz Universität Hannover
Abstract
A bstract : Quantum correlation functions in supersymmetric field theories can be encoded in the Nicolai map. The infinitesimal inverse map provides their response to a change in a coupling constant through a “flow equation”. We investigate the flow in the gravitational constant κ for four-dimensional Poincaré supergravity via its superconformal formulation. By expressing the full superconformal off-shell action as a supervariation we derive a “flow operator” in the effective vierbein theory, whose exponentiation yields the gauge-invariant part of an all-order (inverse) Nicolai map for supergravity. Alas, the BRST gauge fixing adds to this functional differential flow operator a multiplicative term, which ruins its derivational property and therefore jeopardizes its connection with the Nicolai map. We argue and present an example, however, that such multiplicative flow contributions might be rewritable as derivational ones with the help of Wick’s theorem in the free effective theory where the Nicolai-transformed correlators are ultimately evaluated. At least in the Landau gauge, the supergravity flow equation is shown to be regular at κ =0, allowing for a perturbative expansion around Minkowski geometry. Therewith, we have overcome two of the three obstacles met in an earlier attempt towards a Nicolai map for Poincaré supergravity. Finally, we compare with the direct on-shell construction of a Nicolai map to leading order in κ .
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BibTeX
@article{arrighi2026coupling,
title = {{The coupling flow for supergravity}},
author = {Federico Arrighi and Saurish Khandelwal and Olaf Lechtenfeld},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)153},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)153},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - The coupling flow for supergravity
AU - Federico Arrighi
AU - Saurish Khandelwal
AU - Olaf Lechtenfeld
PY - 2026
DA - 2026/10/14
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)153
UR - https://link.springer.com/article/10.1007/JHEP10(2026)153
AB - A bstract : Quantum correlation functions in supersymmetric field theories can be encoded in the Nicolai map. The infinitesimal inverse map provides their response to a change in a coupling constant through a “flow equation”. We investigate the flow in the gravitational constant κ for four-dimensional Poincaré supergravity via its superconformal formulation. By expressing the full superconformal off-shell action as a supervariation we derive a “flow operator” in the effective vierbein theory, whose exponentiation yields the gauge-invariant part of an all-order (inverse) Nicolai map for supergravity. Alas, the BRST gauge fixing adds to this functional differential flow operator a multiplicative term, which ruins its derivational property and therefore jeopardizes its connection with the Nicolai map. We argue and present an example, however, that such multiplicative flow contributions might be rewritable as derivational ones with the help of Wick’s theorem in the free effective theory where the Nicolai-transformed correlators are ultimately evaluated. At least in the Landau gauge, the supergravity flow equation is shown to be regular at κ =0, allowing for a perturbative expansion around Minkowski geometry. Therewith, we have overcome two of the three obstacles met in an earlier attempt towards a Nicolai map for Poincaré supergravity. Finally, we compare with the direct on-shell construction of a Nicolai map to leading order in κ .
SN - 1029-8479
ER -