On Duality Invariant Yang-Mills Theory

TL;DR

This work constructs a manifestly duality-invariant, interacting deformation of Maxwell theory in four dimensions by coupling a 1-form and a 3-form through auxiliary fields and a BRST-quantized framework. A key innovation is replacing the wedge product with a Clifford product and the exterior derivative with the Kähler-Dirac operator $K=d+d^ op$, enabling a duality-symmetric kinetic structure and an associative gauge algebra via $A^{[1]}+A^{[3]}$ and the covariant operator $K_A=K-iA\vee$. The resulting action, expressed in terms of field strengths $F=K_A A^{[1]}$ and $\tilde F=K_A A^{[3]}$, preserves duality between the two gauge copies and yields nonlinear YM-type equations through a local auxiliary $B$-field, circumventing previous no-go results. The theory is formulated as a gauge-fixed BRST system with a consistent gauge structure that can accommodate nonlinear extensions, suggesting a novel route to quantization of duality-symmetric gauge theories and expanding the landscape of associative gauge algebras applicable to non-abelian deformations of Maxwell theory.

Abstract

We provide an explicit construction of a manifestly duality invariant, interacting deformation of Maxwell theory in four dimensions in terms of mutually local, but interacting 1- and 3-forms. Interestingly, our theory is formulated directly as a BRST quantized gauge theory, while the underlying gauge invariant Lagrangian before gauge fixing is obscured. Furthermore, the underlying gauge invariance is based on an associative, rather than a Lie symmetry.