The superconformal formulation of four-dimensional supergravity yields a coupling flow operator that is regular at zero gravitational coupling, clearing two of three obstacles to a Nicolai map.
Universal form of the Nicolai map
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abstract
The nonlocal bosonic theory obtained from integrating out all anticommuting and auxiliary variables in a globally supersymmetric theory is characterized by the Nicolai map. The latter is generated by a coupling flow functional differential operator, which can be canonically constructed when the supersymmetry is realized off-shell. Given any scalar superfield theory, we present a universal formula for both the Nicolai map and its inverse in terms of an ordered exponential of the integrated coupling flow operator. We demonstrate that our formula also holds for supersymmetric gauge theories.
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The coupling flow for supergravity
The superconformal formulation of four-dimensional supergravity yields a coupling flow operator that is regular at zero gravitational coupling, clearing two of three obstacles to a Nicolai map.