Duality for massive spin two theories in arbitrary dimensions

TL;DR

This paper constructs a dual formulation of massive spin two theories in any dimension using the parent Lagrangian approach, clarifying its relation to gauge symmetry methods and confirming the correct degrees of freedom.

Contribution

It introduces a novel dual formulation for massive spin two fields in arbitrary dimensions without auxiliary fields, extending previous four-dimensional results.

Findings

Derived a dual Lagrangian in arbitrary dimensions

Connected the formulation to gauge symmetry approaches

Confirmed the degrees of freedom match the Fierz-Pauli theory

Abstract

Using the parent Lagrangian approach we construct a dual formulation, in the sense originally proposed by Curtright and Freund, of a massive spin two Fierz-Pauli theory in arbitrary dimensions $D$. This is achieved in terms of a mixed symmetry tensor $T_{A[B_{1}B_{2}... B_{D-2}]}$, without the need of auxiliary fields. The relation of this method with an alternative formulation based on a gauge symmetry principle proposed by Zinoviev is elucidated. We show that the latter formulation in four dimensions, with a given gauge fixing together with a definite sequence of auxiliary fields elimination via their equations of motion, leads to the parent Lagrangian already considered by West completed by a Fierz-Pauli mass term, which in turns yields the Curtright-Freund action. This motivates our generalization to arbitrary dimensions leading to the corresponding extension of the four dimensional result. We identify the transverse true degrees of freedom of the dual theory and verify that their number is in accordance with those of the massive Fierz-Pauli field.