Tensor Gauge Fields in Arbitrary Representations of GL(D, ?). Duality and Poincar� Lemma

Abstract

Using a mathematical framework which provides a generalization of the de Rham complex (well-designed for p-form gauge fields), we have studied the gauge structure and duality properties of theories for free gauge fields transforming in arbitrary irreducible representations of GL(D, R). We have proven a generalization of the Poincaré lemma which enables us to solve the above-mentioned problems in a systematic and unified way.

New classes of bi-axially symmetric solutions to four-dimensional Vasiliev higher spin gravity

“…using the generalized Poincare lemma (for example, see [43][44][45]). In other words, an asymptotic observer who sources the bulk using a linearized spin-s Fronsdal field will activate the corresponding component field given above, whose boundary value can thus be identified with a dual conformal field theory source coupled to a conserved spin-s current.…”

Dual gravity and matter

“…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]). …”

“…It was argued in [7] that the condition [7]). A slightly different approach for the introduction of a dual graviton starts from the Riemann tensor and its symmetries [3,6,8]. Dualising the full linearised Riemann tensor R µνρσ on one set of antisymmetric indices gives the tensor…”

“…The (algebraic and differential) identities for the Riemann tensor together with the linearised equations of motion then imply that on-shell [6,8] …”

“…The term˜ µ 1 ...µ D−2 is allowed for since it drops out in S, cf. (8). This paper is organised as follows.…”