Speaker
Description
We present a perturbative construction of the Nicolai map for four-dimensional N = 1 pure supergravity around flat Minkowski space, as an alternative to the coupling-flow-operator approach. Using the second-order formalism and the background-field expansion of the vielbein in the gravitational coupling κ, we derive the on-shell BRST structure and formulate the defining conditions for a Nicolai map expanded in both κ and ℏ. We further recast the construction in a diagrammatic form that generates the most general local ansatz and reduces the problem to coupled nonlinear polynomial constraints. Applying the method to the gauge-fixed Einstein–Hilbert bosonic sector through second order in κ, we show that higher-order consistency is determined by the bosonic input and fixes the admissible lower-order fermionic couplings. These couplings agree with those of pure N = 1 supergravity, indicating a strongly constrained structure underlying the supergravity Nicolai map.
