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 $W_{\mu \nu }$.

15 pages, no figures, typos fixed (eqs (46) and (55)), absence of spin-2 modes pointed out

References in corpus (8)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• Critical Gravity in Four Dimensions
• Ghost-free, finite, fourth order D=3 (alas) gravity
• Critical Points of D-Dimensional Extended Gravities
• Modes of Log Gravity
• Unitarity of spin-2 theories with linearized Weyl symmetry in $D=2+1$
• Dimensional reduction as a method to obtain dual theories for massive spin two in arbitray dimensions

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• The spin jumping in the context of a QCD effective model
• Canonical analysis of Kalb-Ramond-Proca duality
• Duality invariance in massive theories
• Dualities Among Massive, Partially Massless and Shift Symmetric Fields on (A)dS
• Dimensional reduction of the massless limit of the linearized "New Massive Gravity"
• Simple prescription for computing the nonrelativistic interparticle potential energy related to dual models
• A note on higher rank descriptions of massless and massive spin-1 particles
• Mass generation for abelian spin-1 particles via a symmetric tensor
• Duality as a Method to Derive a Gauge Invariant Massive Electrodynamics and New Interactions