Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-05-22
Phys.Rev.D84:045027,2011
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, no figures, typos fixed (eqs (46) and (55)), absence of spin-2 modes pointed out
Scientific paper
10.1103/PhysRevD.84.045027
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 $W_{\mu\nu}$.
Dalmazi D.
Santos R. C.
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