Generalised conformal higher-spin fields in curved backgrounds

Self Cite

For every conformal gauge field h α(n)α(m) in four dimensions, with n ≥ m > 0, a gauge-invariant action is known to exist in arbitrary conformally flat backgrounds. If the Weyl tensor is non-vanishing, however, gauge invariance holds for a pure conformal field in the following cases: (i) n = m = 1 (Maxwell's field) on arbitrary gravitational backgrounds; and (ii) n = m + 1 = 2 (conformal gravitino) and n = m = 2 (conformal graviton) on Bach-flat backgrounds. It is believed that in other cases certain lower-spin fields must be introduced to ensure gauge invariance in Bach-flat backgrounds, although no closedform model has yet been constructed (except for conformal maximal depth fields with spin s = 5/2 and s = 3). In this paper we derive such a gauge-invariant model describing the dynamics of a conformal gauge field h α(3)α coupled to a self-dual two-form. Similar to other conformal higher-spin theories, it can be embedded in an off-shell superconformal gaugeinvariant action. To this end, we introduce a new family of N = 1 superconformal gauge multiplets described by unconstrained prepotentials Υ α(n) , with n > 0, and propose the corresponding gauge-invariant actions on conformally-flat backgrounds. We demonstrate that the n = 2 model, which contains h α(3)α at the component level, can be lifted to a Bach-flat background provided Υ α(2) is coupled to a chiral spinor Ω α. We also propose families of (super)conformal higher-derivative non-gauge actions and new superconformal operators in any curved space. Finally, through considerations based on supersymmetry, we argue that the conformal spin-3 field should always be accompanied by a conformal spin-2 field in order to ensure gauge invariance in a Bach-flat background.

Section: Superconformal Pseudo-graviton Multipletmentioning

confidence: 99%

Section: Superconformal Pseudo-graviton Multipletmentioning

confidence: 99%

Section: Jhep08(2020)068 Introductionmentioning

confidence: 99%

Section: Jhep08(2020)068 Introductionmentioning

confidence: 99%

Section: Jhep08(2020)068 Introductionmentioning

confidence: 99%

See 3 more Smart Citations

New locally (super)conformal gauge models in Bach-flat backgrounds

Kuzenko

Ponds

Raptakis

2020

Self Cite

GJMS-like operators on symmetric 2-tensors and their gravitational duals

Aros

Bugini

Díaz

2023

We study a family of higher-derivative conformal operators $$ {P}_{2k}^{(2)} $$ P 2 k 2 acting on transverse-traceless symmetric 2-tensors on generic Einstein spaces. They are a natural generalization of the well-known construction for scalars.We first provide the alternative description in terms of a bulk Poincaré-Einstein metric by making use of the AdS/CFT dictionary and argue that their holographic dual generically consists of bulk massive gravitons. At one-loop quantum level we put forward a holographic formula for the functional determinant of the higher-derivative conformal operators $$ {P}_{2k}^{(2)} $$ P 2 k 2 in terms of the functional determinant for massive gravitons with standard and alternate boundary conditions. The analogous construction for vectors $$ {P}_{2k}^{(1)} $$ P 2 k 1 is worked out as well and we also rewrite the holographic formula for unconstrained vector and traceless symmetric 2-tensor by decoupling the longitudinal part.Finally, we show that the holographic formula provides the necessary building blocks to address the massless and partially massless bulk gravitons. This is confirmed in four and six dimensions, verifying full agreement with results available in the literature.

Generalised superconformal higher-spin multiplets

Kuzenko

Ponds

Raptakis

2021

Self Cite

We propose generalised $$ \mathcal{N} $$ N = 1 superconformal higher-spin (SCHS) gauge multiplets of depth t, $$ {\Upsilon}_{\alpha (n)\overset{\cdot }{\alpha }(m)}^{(t)} $$ ϒ α n α ⋅ m t , with n ≥ m ≥ 1. At the component level, for t > 2 they contain generalised conformal higher-spin (CHS) gauge fields with depths t − 1, t and t + 1. The supermultiplets with t = 1 and t = 2 include both ordinary and generalised CHS gauge fields. Super-Weyl and gauge invariant actions describing the dynamics of $$ {\Upsilon}_{\alpha (n)\overset{\cdot }{\alpha }(m)}^{(t)} $$ ϒ α n α ⋅ m t on conformally-flat superspace backgrounds are then derived. For the case n = m = t = 1, corresponding to the maximal-depth conformal graviton supermultiplet, we extend this action to Bach-flat backgrounds. Models for superconformal non-gauge multiplets, which are expected to play an important role in the Bach-flat completions of the models for $$ {\Upsilon}_{\alpha (n)\overset{\cdot }{\alpha }(m)}^{(t)} $$ ϒ α n α ⋅ m t , are also provided. Finally we show that, on Bach-flat backgrounds, requiring gauge and Weyl invariance does not always determine a model for a CHS field uniquely.