Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1

TL;DR

This paper explores covariant descriptions of massless and massive spin-2 particles in 2+1 dimensions, introducing new models and analyzing their symmetries, dualities, and consistency within modified gravity frameworks.

Contribution

It demonstrates a novel route from WTDIFF models to scalar tensor NMG and constructs new spin-2 selfdual models using traceless master actions.

Findings

Derived linearized scalar tensor NMG from WTDIFF models.

Constructed two new spin-2 selfdual models.

Identified invariance properties and degrees of freedom in unimodular models.

Abstract

There are two covariant descriptions of massless spin-2 particles in $D=3+1$ via a symmetric rank-2 tensor: the linearized Einstein-Hilbert (LEH) theory and the Weyl plus transverse diffeomorphism (WTDIFF) invariant model. From the LEH theory one can obtain the linearized New Massive Gravity (NMG) in $D=2+1$ via Kaluza-Klein dimensional reduction followed by a dual master action. Here we show that a similar route takes us from the WTDIFF model to a linearized scalar tensor NMG which belongs to a larger class of consistent spin-0 modifications of NMG. We also show that a traceless master action applied to a parity singlet furnishes two new spin-2 selfdual models. Moreover, we examine the singular replacement $h_{\mu\nu} \to h_{\mu\nu} - \eta_{\mu\nu}h/D$ and prove that it leads to consistent massive spin-2 models in $D=2+1$. They include linearized versions of unimodular topologically massive gravity (TMG) and unimodular NMG. Although the free part of those unimodular theories are Weyl invariant, we do not expect any improvement in the renormalizability. Both the linearized K-term (in NMG) and the linearized gravitational Chern-Simons term (in TMG) are invariant under longitudinal reparametrizations $\delta h_{\mu\nu} = \p_{\mu}\p_{\nu}\zeta$ which is not a symmetry of the WTDIFF Einstein-Hilbert term. Therefore, we still have one degree of freedom whose propagator behaves like $1/p^2$ for large momentum.