Conformal (super)gravities with several gravitons

Abstract

We construct consistent interacting gauge theories for M conformal massless spin-2 fields ("Weyl gravitons") with the following properties: (i) in the free limit, each field fulfills the equation B µν = 0, where B µν is the linearized Bach tensor, (ii) the interactions contain no more than four derivatives, just as the free action and (iii) the internal metric for the Weyl gravitons is not positive definite. The interacting theories are obtained by gauging appropriate non-semi-simple extensions of the conformal algebra so(4, 2) with commutative, associative algebras of dimension M . By writing the action in terms of squares of supercurvatures, supersymmetrization is immediate and leads to consistent conformal supergravities with M interacting gravitons.

On conformal higher spin wave operators

“…In particular, the actions of Weyl gravity and conformal supergravity, together with their corresponding wave equations, have been studied in great detail [1][2][3][4][5][6][7][8][9][10][11] as natural extensions of ordinary gravity and supergravity theories. Interest has been also devoted to the corresponding higher spin generalizations [12][13][14][15][16][17][18], not just because of the intriguing role of conformal symmetry.…”

Colourful Poincaré symmetry, gravity and particle actions

“…⊗ a is well-defined since a is abelian, a fact that was also used in the context of (conformal) gravity [18,39]. The Lie algebra sl(2, R) ⊗ a can now be embedded in an associative algebra by extending the first factor and defining the eight-dimensional associative algebra…”

“…(1) E = {λ0, λ1, λ2} with λi•λj = λj •λi = λi+j where λj = 0 for j > 1. One can use the Lie algebra expansion method [38][39][40][41] with this semi-group to obtain a new Lie algebra that is isomorphic to the Lie algebra we describe below. If we assign the hermiticity properties λ † i = λi, then the Lie algebra obtained by the expansion method is exactly the same as we present in (2.13).…”

Nonrelativistic limits of colored gravity in three dimensions

“…[25] for a review and Ref. [26] for an extension to the conformal (super)gravities. In these results, no additional fields besides the graviton (multiplet) are introduced, as opposed to Refs.…”