Consistent deformations of dual formulations of linearized gravity: A no-go result

Abstract

The consistent, local, smooth deformations of the dual formulation of linearized gravity involving a tensor field in the exotic representation of the Lorentz group with Young symmetry type (D − 3, 1) (one column of length D − 3 and one column of length 1) are systematically investigated. The rigidity of the Abelian gauge algebra is first established. We next prove a no-go theorem for interactions involving at most two derivatives of the fields.

Dual gravity and matter

“…This is reminiscent of the findings of [17,18] where it was also argued that the coupling of linearised gravity to dynamical matter sources induces a non-linear completion of the gravity sector. Treating the gravity sector non-linearly, one is however immediately faced with the problem of the obstructions established in [14] when trying to maintain locality and covariance. One possible way out then is to abandon covariance [13], see also [19].…”

“…For linearised gravity in vacuo 1 such a formulation is known to exist [3][4][5][6][7][8][9][10][11][12][13] but a BRST analysis reveals, under rather general assumptions [14], obstructions to extend this to a theory with covariant and local interactions (see also [15]). …”

Exceptional field theory. III.E8(8)

“…, 8, that in three dimensions are dual to the Kaluza-Klein vectors A µ m . As the latter originate from components of the D " 11 metric, this amounts to including in the theory components of a 'dual graviton' [23][24][25][26] at the full non-linear level, something that is considered impossible on the grounds of the no-go theorems in [27,28]. In EFT this problem is resolved due to the presence of the extra E 8p8q gauge symmetry from (1.3).…”

“…We thus introduce the fully covariant curvatures 27) with two-form fields C µν KL p3875q , C µν , and C µν M N , where as in (2.11) the two-form C µν M N is covariantly constrained in the first index. The general variation of these curvatures takes a covariant form,…”

U-duality covariant gravity

“…In D = 3 the Kaluza-Klein vector needs to be dualized into a scalar, which together with the Kaluza-Klein dilaton then parametrizes the SL(2, R)/SO(2) coset space [54]. Since the Kaluza-Klein vector originates from the metric, from a D = 4 perspective this is like dualizing (part of) the graviton, something that due to the no-go results of [55] is usually considered to be impossible. Indeed, previous papers on the subject have unanimously concluded that, presumably for this reason, the D = 3 case cannot be incorporated into a U-duality covariant framework [48,49,56].…”