Spin-1 duality in D dimensions

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).