Standard non-abelian gauge-theory formulation of the constructed duality-invariant model

Determine whether the duality-invariant interacting deformation of Maxwell theory in four dimensions, defined using a 1-form potential A^{[1]}, a 3-form potential A^{[3]}, and an auxiliary multiform B with interactions built from the Kähler-Dirac operator K_A = K − i A ∨ (where K = d + d† and ∨ is the Clifford product) and action S = ∫ [1/2 (A, (K_A)^2 A) + i (K_A A, B)], admits a formulation as a standard non-abelian gauge theory in the usual sense with a gauge-invariant Lagrangian prior to gauge fixing.

Background

The paper constructs a manifestly duality-invariant, interacting deformation of Maxwell theory in four dimensions by coupling mutually local 1- and 3-form potentials with auxiliary fields. Interactions are introduced via the Clifford product on differential forms and the Kähler-Dirac operator, yielding a BRST-quantized description that circumvents known no-go results for local, duality-invariant formulations of non-abelian gauge theories.

In this framework, gauge invariance is realized through an associative structure rather than purely Lie algebraic brackets, and the interacting theory is formulated directly at the level of gauge fixing and BRST quantization. The authors explicitly state uncertainty about whether this model can be recast as a conventional non-abelian gauge theory with a gauge-invariant Lagrangian before gauge fixing, making the existence of such a standard formulation an open question.