Precise structure of the non-Abelian magnetic dual at k=0

Determine the precise structure of the non-Abelian magnetic dual theory in the k=0 regime derived from the three-dimensional N=2 superspace master partition function, where the electric description reduces to pure Yang–Mills and the magnetic side becomes an infinite tower of commutator interactions subject to a covariant flatness condition; provide a closed-form or fully explicit formulation of this magnetic dual and characterise its dynamics.

Background

The paper constructs a single off-shell three-dimensional N=2 superspace master partition function that realises S-duality between Maxwell–Chern–Simons theory and a Deser–Jackiw massive vector plus a decoupled Chern–Simons sector, and extends the framework to a non-Abelian U(N) gauge group. The construction is designed to capture global (holonomy) data via a group-valued Stueckelberg multiplet, yielding a genuinely quantum duality.

In the non-Abelian case with k=0, the electric side becomes pure Yang–Mills, while the magnetic side does not admit a simple closed-form description: it turns into an infinite tower of commutator interactions governed by a covariant flatness condition, resembling a highly deformed principal chiral model. The authors state that the magnetic dual is only implicit and that fully determining its structure remains open.