scholarly journals Matter-free higher spin gravities in 3D: Partially-massless fields and general structure

2020 ◽  
Vol 102 (6) ◽  
Author(s):  
Maxim Grigoriev ◽  
Karapet Mkrtchyan ◽  
Evgeny Skvortsov
Keyword(s):  
General Structure ◽  
Higher Spin ◽  
Massless Fields

scholarly journals ANTI-DE SITTER GRAVITY FROM BF–CHERN–SIMONS–HIGGS THEORIES

2002 ◽  
Vol 17 (32) ◽  
pp. 2095-2103 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Isometry Group ◽  
Star Product ◽  
Constant Term ◽  
Higgs Potential ◽  
De Sitter ◽  
Potential Term ◽  
Higher Spin ◽  
Noncommutative Gravity ◽  
Chern Simons ◽  
Massless Fields

It is shown that an action inspired from a BF and Chern–Simons model, based on the AdS4 isometry group SO(3,2), with the inclusion of a Higgs potential term, furnishes the MacDowell–Mansouri–Chamseddine–West action for gravity, with a Gauss–Bonnet and cosmological constant term. The AdS4 space is a natural vacuum of the theory. Using Vasiliev's procedure to construct higher spin massless fields in AdS spaces and a suitable star product, we discuss the preliminary steps to construct the corresponding higher-spin action in AdS4 space representing the higher spin extension of this model. Brief remarks on noncommutative gravity are made.

scholarly journals AdS3/AdS2 degression of massless particles

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Konstantin Alkalaev ◽  
Alexander Yan
Keyword(s):  
Massless Particle ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Spin Representation ◽  
Theoretical Terms ◽  
Finite Spectrum ◽  
Branching Rules ◽  
Higher Spin ◽  
Massless Fields ◽  
Kaluza Klein

Abstract We study a 3d/2d dimensional degression which is a Kaluza-Klein type mechanism in AdS3 space foliated into AdS2 hypersurfaces. It is shown that an AdS3 massless particle of spin s = 1, 2, …, ∞ degresses into a couple of AdS2 particles of equal energies E = s. Note that the Kaluza-Klein spectra in higher dimensions are always infinite. To formulate the AdS3/AdS2 degression we consider branching rules for AdS3 isometry algebra o(2,2) representations decomposed with respect to AdS2 isometry algebra o(1,2). We find that a given o(2,2) higher-spin representation lying on the unitary bound (i.e. massless) decomposes into two equal o(1,2) modules. In the field-theoretical terms, this phenomenon is demonstrated for spin-2 and spin-3 free massless fields. The truncation to a finite spectrum can be seen by using particular mode expansions, (partial) diagonalizations, and identities specific to two dimensions.

HIGHER-SPIN SYMMETRY IN ONE AND TWO DIMENSIONS (II)

1989 ◽  
Vol 04 (27) ◽  
pp. 2649-2665 ◽  
Author(s):  
E.S. FRADKIN ◽  
V. Ya. LINETSKY
Keyword(s):  
Higher Spin Symmetry ◽  
General Structure ◽  
Virasoro Algebra ◽  
Spin Symmetry ◽  
Two Dimensions ◽  
Higher Spin

Constructed are conformal higher spin superalgebras in one and two dimensions, which contain the Virasoro algebra as a subalgebra. The general structure of these superalgebras is investigated.

scholarly journals Three-point functions of higher-spin spinor current multiplets in $$ \mathcal{N} $$ = 1 superconformal theory

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Evgeny I. Buchbinder ◽  
Jessica Hutomo ◽  
Sergei M. Kuzenko
Keyword(s):  
Correlation Function ◽  
General Structure ◽  
Complex Coefficient ◽  
Precise Form ◽  
Superconformal Symmetry ◽  
Arbitrary Rank ◽  
Higher Spin ◽  
Single Complex ◽  
Conserved Current ◽  
Spinor Current

Abstract In this paper, we study the general form of three-point functions of conserved current multiplets Sα(k) = S(α1…αk) of arbitrary rank in four-dimensional $$ \mathcal{N} $$ N = 1 superconformal theory. We find that the correlation function of three such operators $$ \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\beta \left(k+l\right)}\left({z}_2\right){\overline{S}}_{\dot{\gamma}(l)}\left({z}_3\right)\right\rangle $$ S ¯ α ̇ k z 1 S β k + l z 2 S ¯ γ ̇ l z 3 is fixed by the superconformal symmetry up to a single complex coefficient though the precise form of the correlator depends on the values of k and l. In addition, we present the general structure of mixed correlators of the form $$ \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\alpha (k)}\left({z}_2\right)L\left({z}_3\right)\right\rangle $$ S ¯ α ̇ k z 1 S α k z 2 L z 3 and $$ \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\alpha (k)}\left({z}_2\right){J}_{\gamma \dot{\gamma}}\left({z}_3\right)\right\rangle $$ S ¯ α ̇ k z 1 S α k z 2 J γ γ ̇ z 3 , where L is the flavour current multiplet and $$ {J}_{\gamma \dot{\gamma}} $$ J γ γ ̇ is the supercurrent.

scholarly journals A compendium of sphere path integrals

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Y.T. Albert Law
Keyword(s):  
Standard Procedure ◽  
Path Integrals ◽  
Symmetric Tensor ◽  
Arbitrary Spin ◽  
Tensor Fields ◽  
Arbitrary Integer ◽  
Integer Spin ◽  
Higher Spin ◽  
Detailed Derivation ◽  
Massless Fields

Abstract We study the manifestly covariant and local 1-loop path integrals on Sd+1 for general massive, shift-symmetric and (partially) massless totally symmetric tensor fields of arbitrary spin s ≥ 0 in any dimensions d ≥ 2. After reviewing the cases of massless fields with spin s = 1, 2, we provide a detailed derivation for path integrals of massless fields of arbitrary integer spins s ≥ 1. Following the standard procedure of Wick-rotating the negative conformal modes, we find a higher spin analog of Polchinski’s phase for any integer spin s ≥ 2. The derivations for low-spin (s = 0, 1, 2) massive, shift-symmetric and partially massless fields are also carried out explicitly. Finally, we provide general prescriptions for general massive and shift-symmetric fields of arbitrary integer spins and partially massless fields of arbitrary integer spins and depths.

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 Double copy structure of parity-violating CFT correlators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Flat Space ◽  
Field Theories ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Spin ◽  
Space Limit ◽  
Double Copy ◽  
Conserved Currents ◽  
Massless Fields

Abstract We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators. Splitting up the CFT correlator into two parts — called homogeneous and non-homogeneous — we show that double copy relations exist for each part separately. We arrive at similar conclusions regarding double copy structures using tree-level correlators of massless fields in dS4. We also discuss the flat space limit of these correlators. We further extend the double copy analysis to correlators involving higher-spin conserved currents, which suggests that the spin-s current correlator can be thought of as s copies of the spin one current correlator.

Sign in / Sign up

Export Citation Format

Share Document