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.
An improved Nicolai map for super Yang-Mills theory
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abstract
Adding a topological theta term to the action of $\mathcal{N}{=}\,1$ $D{=}4$ super Yang-Mills theory modifies its Nicolai map. For the BPS value of the theta angle a chiral version of the map emerges, which allows for a considerable simplification compared to the non-chiral formulation. We exhibit these improvements to all orders in perturbation theory and compute the map to fourth order in the coupling on the Laudau-gauge hypersurface. The second-order contribution vanishes, and antisymmetrizations are more manifest. All checks are verified to third 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.