scholarly journals Higher-spin Cotton tensors and massive gauge-invariant actions in AdS3

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Sergei M. Kuzenko ◽  
Michael Ponds
Keyword(s):  
Three Dimensional ◽  
Closed Form Expression ◽  
De Sitter ◽  
Gauge Invariant ◽  
Covariant Derivatives ◽  
Dimensional Spacetime ◽  
Shell Analysis ◽  
Higher Spin ◽  
Conformal Gauge ◽  
Cotton Tensor

Abstract In a conformally flat three-dimensional spacetime, the linearised higher-spin Cotton tensor ℭα(n)(h) is the unique conserved conformal current which is a gauge-invariant descendant of the conformal gauge prepotential hα(n). The explicit form of ℭα(n)(h) is well known in Minkowski space. Here we solve the problem of extending the Minkowskian result to the case of anti-de Sitter (AdS) space and derive a closed-form expression for ℭα(n)(h) in terms of the AdS Lorentz covariant derivatives. It is shown that every conformal higher-spin action $$ {S}_{\mathrm{CS}}^{(n)}\left[h\right]\propto \int {\mathrm{d}}^3{xeh}^{\alpha (n)}{\mathrm{\mathfrak{C}}}_{\alpha (n)}(h) $$ S CS n h ∝ ∫ d 3 xeh α n ℭ α n h factorises into a product of (n − 1) first-order operators that are associated with the spin-n/2 partially massless AdS values. Our findings greatly facilitate the on-shell analysis of massive higher-spin gauge-invariant actions in AdS3. The main results are extended to the case of $$ \mathcal{N} $$ N = 1 AdS supersymmetry. In particular, we derive simple expressions for the higher-spin super-Cotton tensors in AdS3.

scholarly journals AdS superprojectors

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
E. I. Buchbinder ◽  
D. Hutchings ◽  
S. M. Kuzenko ◽  
M. Ponds
Keyword(s):  
Shell Model ◽  
Differential Operators ◽  
Second Order ◽  
Projection Operators ◽  
De Sitter ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Higher Spin

Abstract Within the framework of $$ \mathcal{N} $$ N = 1 anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)}:= {\mathfrak{V}}_{\left(\alpha 1\dots \alpha m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} $$ V α m α ⋅ n ≔ V α 1 … αm α ⋅ 1 … α ⋅ n on AdS superspace, with m and n non-negative integers, the corresponding superprojector turns $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)} $$ V α m α ⋅ n into a multiplet with the properties of a conserved conformal supercurrent. It is demonstrated that the poles of such superprojectors correspond to (partially) massless multiplets, and the associated gauge transformations are derived. We give a systematic discussion of how to realise the unitary and the partially massless representations of the $$ \mathcal{N} $$ N = 1 AdS4 superalgebra $$ \mathfrak{osp} $$ osp (1|4) in terms of on-shell superfields. As an example, we present an off-shell model for the massive gravitino multiplet in AdS4. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.

scholarly journals PROMOTING FINITE TO INFINITE SYMMETRIES: THE (3 + 1)-DIMENSIONAL ANALOGUE OF THE VIRASORO ALGEBRA AND HIGHER-SPIN FIELDS

2000 ◽  
Vol 15 (14) ◽  
pp. 939-944 ◽  
Author(s):  
M. CALIXTO
Keyword(s):  
Gauge Theories ◽  
Conformal Symmetry ◽  
Virasoro Algebra ◽  
De Sitter ◽  
Infinite Dimensional ◽  
Higher Spin ◽  
Spin Fields ◽  
Conformal Gauge ◽  
Matter Fields ◽  
Integrable Field

Infinite enlargements of finite pseudo-unitary symmetries are explicitly provided in this letter. The particular case of u (2, 2) ≃ so (4, 2) ⊕ u (1) constitutes a (Virasoro-like) infinite-dimensional generalization of the (3 + 1) -dimensional conformal symmetry, in addition to matter fields with all conformal spins. These algebras provide a new arena for integrable field models in higher dimensions; for example, anti-de Sitter and conformal gauge theories of higher-so(4, 2)-spin fields. A proposal for a noncommutative geometrical interpretation of space is also outlined.

scholarly journals Extended superconformal higher-spin gauge theories in four dimensions

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Sergei M. Kuzenko ◽  
Emmanouil S. N. Raptakis
Keyword(s):  
Gauge Theories ◽  
Conformally Flat ◽  
De Sitter ◽  
Conformal Supergravity ◽  
Gauge Invariant ◽  
Four Dimensions ◽  
Higher Spin ◽  
Shell Formulation ◽  
Conserved Currents ◽  
Field Strengths

Abstract Using the off-shell formulation for $$ \mathcal{N} $$ N = 2 conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved background and present their associated unconstrained gauge prepotentials. The latter are used to construct locally superconformal chiral actions, which are demonstrated to be gauge invariant in arbitrary conformally flat backgrounds. The main $$ \mathcal{N} $$ N = 2 results are then generalised to the $$ \mathcal{N} $$ N -extended case. We also present the gauge-invariant field strengths for on-shell massless higher-spin $$ \mathcal{N} $$ N = 2 supermultiplets in anti-de Sitter space. These field strengths prove to furnish representations of the $$ \mathcal{N} $$ N = 2 superconformal group.

scholarly journals AdS (super)projectors in three dimensions and partial masslessness

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Daniel Hutchings ◽  
Sergei M. Kuzenko ◽  
Michael Ponds
Keyword(s):  
Isometry Group ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Irreducible Representations ◽  
Projection Operators ◽  
De Sitter ◽  
Arbitrary Integer ◽  
Higher Spin ◽  
Casimir Operators ◽  
Massless Fields

Abstract We derive the transverse projection operators for fields with arbitrary integer and half-integer spin on three-dimensional anti-de Sitter space, AdS3. The projectors are constructed in terms of the quadratic Casimir operators of the isometry group SO(2, 2) of AdS3. Their poles are demonstrated to correspond to (partially) massless fields. As an application, we make use of the projectors to recast the conformal and topologically massive higher-spin actions in AdS3 into a manifestly gauge-invariant and factorised form. We also propose operators which isolate the component of a field that is transverse and carries a definite helicity. Such fields correspond to irreducible representations of SO(2, 2). Our results are then extended to the case of $$ \mathcal{N} $$ N = 1 AdS3 supersymmetry.

scholarly journals Gauge theory of the Maxwell and semi-simple extended (anti) de Sitter algebra

2021 ◽  
pp. 2150075
Author(s):  
Salih Kibaroğlu ◽  
Oktay Cebecioğlu
Keyword(s):  
Gauge Condition ◽  
Cosmological Term ◽  
Simple Extension ◽  
Extended Version ◽  
De Sitter ◽  
Field Equations ◽  
Gauge Invariant ◽  
Dimensional Spacetime ◽  
Torsion Free ◽  
Model Action

In this paper, a semi-simple and Maxwell extension of the (anti) de Sitter algebra is constructed. Then, a gauge-invariant model has been presented by gauging the Maxwell semi-simple extension of the (anti) de Sitter algebra. We firstly construct a Stelle–West-like model action for five-dimensional spacetime in which the effects of spontaneous symmetry breaking have been taken into account. In doing so, we get an extended version of Einstein’s field equations. Next, we decompose the five-dimensional extended Lie algebra and establish a MacDowell–Mansouri-like action that contains the Einstein–Hilbert term, the cosmological term as well as new terms coming from Maxwell extension in four-dimensional spacetime where the torsion-free condition is assumed. Finally, we have shown that both models are equivalent for an appropriately chosen gauge condition.

scholarly journals Chemical potentials in three-dimensional higher spin anti-de Sitter gravity

2013 ◽  
Vol 2013 (12) ◽  
Author(s):  
Marc Henneaux ◽  
Alfredo Pérez ◽  
David Tempo ◽  
Ricardo Troncoso
Keyword(s):  
Three Dimensional ◽  
De Sitter ◽  
Chemical Potentials ◽  
Higher Spin

scholarly journals Higher spin de Sitter Hilbert space

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Dionysios Anninos ◽  
Frederik Denef ◽  
Ruben Monten ◽  
Zimo Sun
Keyword(s):  
Hilbert Space ◽  
De Sitter ◽  
Higher Spin

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Cosmic hylomorphism

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
William M. R. Simpson
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Bohmian Mechanics ◽  
Temporal Development ◽  
Primitive Ontology ◽  
Law Of Nature ◽  
Dimensional Spacetime ◽  
Global Configuration ◽  
Quantum Phenomena ◽  
Three Dimensional Space

AbstractThe primitive ontology approach to quantum mechanics seeks to account for quantum phenomena in terms of a distribution of matter in three-dimensional space (or four-dimensional spacetime) and a law of nature that describes its temporal development. This approach to explaining quantum phenomena is compatible with either a Humean or powerist account of laws. In this paper, I offer a powerist ontology in which the law is specified by Bohmian mechanics for a global configuration of particles. Unlike in other powerist ontologies, however, this law is not grounded in a structural power that is instantiated by the global configuration. Instead, I combine the primitive ontology approach with Aristotle’s doctrine of hylomorphism to create a new metaphysical model, in which the cosmos is a hylomorphic substance with an intrinsic power to choreograph the trajectories of the particles.

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