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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2605.29990 |
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| _version_ | 1866914614306930688 |
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| author | Chae, Ji-Seong Jang, Hun Lee, Junhyeok |
| author_facet | Chae, Ji-Seong Jang, Hun Lee, Junhyeok |
| contents | We develop a perturbative, diagrammatic framework for constructing Nicolai maps and apply it to four-dimensional $\mathcal{N}=1$ 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 $\hbar$, 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 $\mathcal{N}=1$ supersymmetric completion, Poincaré supergravity, supporting Nicolai's characterization of supersymmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29990 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perturbative Nicolai-Map Diagrammatics: Application to Poincaré Supergravity Chae, Ji-Seong Jang, Hun Lee, Junhyeok High Energy Physics - Theory We develop a perturbative, diagrammatic framework for constructing Nicolai maps and apply it to four-dimensional $\mathcal{N}=1$ 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 $\hbar$, 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 $\mathcal{N}=1$ supersymmetric completion, Poincaré supergravity, supporting Nicolai's characterization of supersymmetry. |
| title | Perturbative Nicolai-Map Diagrammatics: Application to Poincaré Supergravity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.29990 |