Dimensional reduction as a method to obtain dual theories for massive spin two in arbitray dimensions

Abstract

Using the parent Lagrangian method together with a dimensional reduction from $D$ to $(D-1)$ dimensions we construct dual theories for massive spin two fields in arbitrary dimensions in terms of a mixed symmetry tensor $T_{A[A_1{A}_2...A_{D-2}]}$. Our starting point is the well studied massless parent action in dimension $D$. The resulting massive Stueckelberg-like parent actions in $(D-1)$ dimensions inherits all the gauge symmetries of the original massless action and can be gauge fixed in two alternative ways, yielding the possibility of having either a parent action with a symmetric or a non-symmetric Fierz-Pauli field $e_{AB}$. Even though the dual sector in terms of the standard spin two field includes only the symmetrical part $e_{\{AB\}}$ in both cases, these two possibilities yield different results in terms of the alternative dual field $T_{A[A_1{A}_2...A_{D-2}]}$. In particular, the non-symmetric case reproduces the Freund-Curtright action as the dual to the massive spin two field action in four dimensions.

14 pages, no figures, RevTex 4. Some clarifying comments and references have been added

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• Spin-2 twisted duality in (A)dS
• Duality invariance in massive theories
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• Dimensional reduction of the massless limit of the linearized "New Massive Gravity"
• More on dual actions for massive spin-2 particles
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