Quantum M2→2Λ/3 discontinuity for massive gravity with a Λ term

M.J Duff,H Sati,James T Liu

doi:10.1016/s0370-2693(01)00909-1

Abstract

In a previous paper we showed that the absence of the van Dam-Veltman-Zakharov discontinuity as M^2 -> 0 for massive spin-2 with a Lambda term is an artifact of the tree approximation, and that the discontinuity reappears at one loop, as a result of going from five degrees of freedom to two. In this paper we show that a similar classical continuity but quantum discontinuity arises in the "partially massless" limit M^2 -> 2Lambda/3, as a result of going from five degrees of freedom to four.

Highlights

In a previous paper [1], we showed that the absence [2,3,4] of the van Dam-VeltmanZakharov discontinuity [5,6] for massive spin-2 with a Λ term is an artifact of the tree approximation, and that the discontinuity reappears at one loop
The presence of a cosmological constant allows for new gauge invariances of massive higher spin theories, yielding a rich structure of “partially massless” theories with reduced degrees of freedom [7]
In this paper we extend the result of [1] to the partially massless theory and show that a discontinuity first arises at the quantum level as M2 → 2Λ/3

Summary

Typeset using REVTEX

In a previous paper [1], we showed that the absence [2,3,4] of the van Dam-VeltmanZakharov discontinuity [5,6] for massive spin-2 with a Λ term is an artifact of the tree approximation, and that the discontinuity reappears at one loop This result may be understood as follows. For spin-2 a single gauge invariance shows up at the value M2 = 2Λ/3, yielding a partially massless theory with four degrees of freedom [8,9,10]. This gauge invariance was first noted in [8], and results in a partially massless de Sitter theory with four degrees of freedom and propagation along the light cone. It requires that the coupling to matter be via a tracelees energy-momentum tensor

We wish to consider the generating functional

Even for a de Sitter background with constant curvature