Interacting spin-2 fields in three dimensions

Abstract

Using the frame formulation of multi-gravity in three dimensions, we show that demanding the presence of secondary constraints which remove the Boulware-Deser ghosts restricts the possible interaction terms of the theory and identifies invertible frame field combinations whose effective metric may consistently couple to matter. The resulting ghost-free theories can be represented by theory graphs which are trees. In the case of three frame fields, we explicitly show that the requirement of positive masses and energies for the bulk spin-2 modes in AdS$_3$ is consistent with a positive central charge for the putative dual CFT$_2$.Comment: 26 pages, 3 figures, v2: minor changes, matches published versio

Vielbein to the rescue? Breaking the symmetric vielbein condition in massive gravity and multigravity

“…As a result we confirm that cycles of interactions in multigravity break the symmetric vielbein condition and also lead to a BD ghost in the unconstrained vielbein language. This is consistent with the conclusions of [44].…”

“…As such the equivalence with the metric is broken, leaving open the possibility that the vielbein formulation could be better behaved. To better understand the implications of breaking the symmetric vielbein condition, we consider a specific example in D ¼ 3 dimensions (see also [44]), where for simplicity we consider the "massive gravity" limit of trigravity where one of the vielbein acts as a reference metric f A . We are dealing with a loop as long as none of the coefficients c i vanish.…”

Multimetric supergravities

“…Enforcing the symmetricity condition (2.2) represents one of the delicate points of the construction and allows to further restrict the class of allowed potentials. Indeed, further requirements are to be imposed on the coupling tensor T I 1 ...I D so as to avoid the appearance of ghosts [29,31,32]. In particular, whenever N ≥ 3 no more than two different vielbeins may appear simultaneously in the same vertex, while chains of vertices that connect different vielbeins so as to close a loop are also to be excluded.…”

On the Faddeev–Jackiw symplectic framework for topologically massive gravity

“…Theories of interacting spin-2 fields, such as massive gravity, have been considerably studied in the literature, with particular focus on their symmetries and physical degrees of freedom [1][2][3][4][5][6][7][8][9][10][11][12]. The construction of a unitary and renormalizable theory of gravity with propagating degrees of freedom has been a long-sought goal toward our understanding of gravitation.…”