Spin-1 duality in $D$-dimensions

TL;DR

This paper explores a duality in D-dimensional spacetime between Maxwell theory and a higher-order symmetric tensor model, revealing connections to critical gravity and extending to massive cases.

Contribution

It introduces a novel duality between Maxwell theory and a symmetric tensor model in D dimensions, linking flat and curved spacetime formulations and connecting to critical gravity.

Findings

Duality between Maxwell theory and a symmetric tensor model in D dimensions.

Connection between critical gravity in D=4 and Maxwell theory with Ricci coupling.

Explicit duality for massive Maxwell-Proca theory in flat spacetime.

Abstract

It is known that the Maxwell theory in $D$ dimensions can be written in a first order form (in derivatives) by introducing a totally antisymmetric field which leads to a $(D-3)$-form dual theory. Remarkably, one can replace the antisymmetric field by a symmetric rank two tensor ($W_{\mu\nu}=W_{\nu\mu}$). Such master action establishes the duality between the Maxwell-theory and a fourth order higher rank model in a $D$-dimensional flat space time. A naive generalization to the curved space shows a connection between the recently found D=4 critical gravity and the Maxwell theory plus a coupling term to the Ricci tensor ($R_{\mu\nu}A^{\mu}A^{\nu}$). The mass of the spin-1 particle which appears in the D=4 critical gravity linearized around anti-de Sitter space is the same one obtained from the Ricci coupling term. We also work out, in flat space time, the explicitly massive case (Maxwell-Proca) which is dual to a second order theory for $W_{\mu\nu}$.