Topologically massive higher spin gauge theories

Abstract

We elaborate on conformal higher-spin gauge theory in three-dimensional (3D) curved space. For any integer n > 2 we introduce a conformal spin-n 2 gauge field h (n) = h α 1 ...αn (with n spinor indices) of dimension (2 − n/2) and argue that it possesses a Weyl primary descendant C (n) of dimension (1 + n/2). The latter proves to be divergenceless and gauge invariant in any conformally flat space. Primary fields C (3) and C (4) coincide with the linearised Cottino and Cotton tensors, respectively. Associated with C (n) is a Chern-Simons-type action that is both Weyl and gauge invariant in any conformally flat space. These actions, which for n = 3 and n = 4 coincide with the linearised actions for conformal gravitino and conformal gravity, respectively, are used to construct gauge-invariant models for massive higher-spin fields in Minkowski and anti-de Sitter space. In the former case, the higher-derivative equations of motion are shown to be equivalent to those first-order equations which describe the irreducible unitary massive spin-n 2 representations of the 3D Poincaré group. Finally, we develop N = 1 supersymmetric extensions of the above results.

Field theories with (2,0) AdS supersymmetry in N=1 AdS superspace

“…The action (3.32) coincides with the off-shell N = 1 supersymmetric action for massless half-integer superspin in AdS in the form given in [14]. This supersymmetric gauge theory in AdS 3|2 was described in [14]. Its flat-superspace limit was presented earlier in [26].…”

“…where Q is the quadratic Casimir operator of the 3D N = 1 AdS supergroup (A.9) . The action (3.32) coincides with the off-shell N = 1 supersymmetric action for massless half-integer superspin in AdS in the form given in [14]. This supersymmetric gauge theory in AdS 3|2 was described in [14].…”

“…(2.16a) -(2.16d), upon N = 1 projection. Thus (ξ a , ξ α , λ ab ) parametrise the infinitesimal isometries of AdS 3|2 [3] (see also [14]).…”

“…The action (3.36) defines a new N = 1 supersymmetric higher-spin theory which did not appear in [14,21,26] even in the super-Poincaré case.…”

“…There are at least two motivations for pursuing such an application. Firstly, certain theoretical arguments imply that there exist more general off-shell massless higher-spin N = 1 supermultiplets in AdS 3 than those described in [14]. Secondly, N = 1 supermultiplets of conserved higher-spin currents have never been constructed in AdS 3 (except for the superconformal multiplets of conserved currents in Minkowski superspace [15] which can readily be lifted to AdS 3 ).…”