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

TL;DR

This paper develops dual theories for massive spin two fields in arbitrary dimensions using dimensional reduction and parent Lagrangian methods, revealing different dual formulations depending on gauge fixing choices.

Contribution

It introduces a novel approach to construct dual theories for massive spin two fields in any dimension via dimensional reduction from massless actions.

Findings

Reproduces the Freund-Curtright action as a dual in four dimensions.

Shows gauge fixing leads to different dual formulations.

Provides a unified framework for dual theories in arbitrary 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.