Perturbative Nicolai-Map Diagrammatics: Application to Poincaré Supergravity
Abstract
We develop a perturbative, diagrammatic framework for constructing Nicolai maps and apply it to four-dimensional 𝒩=1 Poincaré supergravity expanded around flat Minkowski space. It provides an alternative to the coupling-flow-operator construction, which faces several obstructions when extended to local supersymmetry. Expanding the bosonic effective action and the Nicolai map jointly in the gravitational coupling κ and the loop-counting parameter ℏ, we derive the Nicolai-map defining conditions, i.e. the free-action and determinant-matching conditions, order by order. The diagrammatics enumerates all admissible local terms in the Nicolai-map ansatz from the effective-action diagrams and reduces the construction to a finite system of nonlinear polynomial equations. Carried through order κ2, the resulting constraints are found to be independent of the detailed bosonic input and hierarchical, order-κ2 consistency further restricting the order-κ data. A consistent Nicolai-map construction for the Einstein--Hilbert graviton sector is found to require the Rarita--Schwinger gravitino already at this order: Einstein gravity admits a Nicolai map only through its 𝒩=1 supersymmetric completion, Poincaré supergravity, supporting Nicolai's characterization of supersymmetry.
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BibTeX
@misc{chae2026perturbative,
title = {{Perturbative Nicolai-Map Diagrammatics: Application to Poincaré Supergravity}},
author = {Ji-Seong Chae and Hun Jang and Junhyeok Lee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.29990},
eprint = {2605.29990},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.29990},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Perturbative Nicolai-Map Diagrammatics: Application to Poincaré Supergravity
AU - Ji-Seong Chae
AU - Hun Jang
AU - Junhyeok Lee
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2605.29990
UR - https://arxiv.org/abs/2605.29990
AB - We develop a perturbative, diagrammatic framework for constructing Nicolai maps and apply it to four-dimensional 𝒩=1 Poincaré supergravity expanded around flat Minkowski space. It provides an alternative to the coupling-flow-operator construction, which faces several obstructions when extended to local supersymmetry. Expanding the bosonic effective action and the Nicolai map jointly in the gravitational coupling κ and the loop-counting parameter ℏ, we derive the Nicolai-map defining conditions, i.e. the free-action and determinant-matching conditions, order by order. The diagrammatics enumerates all admissible local terms in the Nicolai-map ansatz from the effective-action diagrams and reduces the construction to a finite system of nonlinear polynomial equations. Carried through order κ^2, the resulting constraints are found to be independent of the detailed bosonic input and hierarchical, order-κ^2 consistency further restricting the order-κ data. A consistent Nicolai-map construction for the Einstein--Hilbert graviton sector is found to require the Rarita--Schwinger gravitino already at this order: Einstein gravity admits a Nicolai map only through its 𝒩=1 supersymmetric completion, Poincaré supergravity, supporting Nicolai's characterization of supersymmetry.
ER -