An improved Nicolai map for super Yang-Mills theory

TL;DR

This paper develops an improved Nicolai map for super Yang-Mills theory with a topological theta term, simplifying calculations especially at the BPS theta angle, and verifies the improvements through fourth-order perturbative computations.

Contribution

It introduces a chiral Nicolai map for super Yang-Mills theory at the BPS theta angle, simplifying the perturbative expansion and providing explicit calculations up to fourth order.

Findings

Second-order contribution vanishes

Antisymmetrizations are more manifest

Checks verified up to third order

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.