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.
Construction method for the Nicolai map in supersymmetric Yang-Mills theories
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Recently, a universal formula for the Nicolai map in terms of a coupling flow functional differential operator was found. We present the full perturbative expansion of this operator in Yang-Mills theories where supersymmetry is realized off-shell. Given this expansion, we develop a straightforward method to compute the explicit Nicolai map to any order in the gauge coupling. Our work extends the previously known construction method from the Landau gauge to arbitrary gauges and from the gauge hypersurface to the full gauge-field configuration space. As an example, we present the map in the axial gauge to the second order.
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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.