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 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 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.

Energy loss of a heavy particle near a three-dimensional charged hairy black hole

2014 ◽  
Vol 92 (11) ◽  
pp. 1481-1484 ◽  
Author(s):  
J. Naji ◽  
S. Heydari ◽  
A. Amjadi
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Energy Loss ◽  
Heavy Particle ◽  
Three Dimensional ◽  
Three Dimensions ◽  
De Sitter ◽  
Conformal Field ◽  
Scalar Charge ◽  
Hairy Black Hole

In this paper, we consider a charged black hole in three dimensions with a scalar charge and discuss energy loss of a heavy particle moving near the black hole horizon. This analysis is useful when anti-de Sitter space – conformal field theory correspondence is applied. We find that an electric charge of a black hole increases the drag force but a scalar charge decreases it.

scholarly journals GEOMETRIC MODULAR ACTION AND SPACETIME SYMMETRY GROUPS

2000 ◽  
Vol 12 (04) ◽  
pp. 475-560 ◽  
Author(s):  
DETLEV BUCHHOLZ ◽  
OLAF DREYER ◽  
MARTIN FLORIG ◽  
STEPHEN J. SUMMERS
Keyword(s):  
Isometry Group ◽  
Three Dimensional ◽  
Algebraic Characterization ◽  
Symmetry Groups ◽  
De Sitter ◽  
Vacuum States ◽  
Point Transformations ◽  
Projective Representations ◽  
Modular Covariance

A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides these groups with projective representations. Under suitable additional conditions, these groups induce groups of point transformations on these space-times, which may be interpreted as symmetry groups. The consequences of this condition are studied in detail in application to two concrete space-times — four-dimensional Minkowski and three-dimensional de Sitter spaces — for which it is shown how this condition characterizes the states invariant under the respective isometry group. An intriguing new algebraic characterization of vacuum states is given. In addition, the logical relations between the condition proposed in this paper and the condition of modular covariance, widely used in the literature, are completely illuminated.

scholarly journals Canonical quantization of the covariant fields on de Sitter space–times

2018 ◽  
Vol 33 (08) ◽  
pp. 1830007 ◽  
Author(s):  
Ion I. Cotaescu
Keyword(s):  
Isometry Group ◽  
Canonical Quantization ◽  
Principal Series ◽  
De Sitter Space ◽  
Fermion Mass ◽  
Dirac Field ◽  
De Sitter ◽  
Covariant Quantum ◽  
Covariant Representations ◽  
Casimir Operators

The properties of the covariant quantum fields on de Sitter space–times are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field, it is shown that the spinor covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the [Formula: see text] group, transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down finding that the covariant representations are equivalent with unitary irreducible ones from the principal series whose canonical weights are determined by the fermion mass and spin.

scholarly journals Off-shell higher-spin fields in AdS4 and external currents

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
N.G. Misuna
Keyword(s):  
Spin System ◽  
Wave Equations ◽  
Current System ◽  
De Sitter ◽  
Arbitrary Integer ◽  
Shell System ◽  
Integer Spin ◽  
Higher Spin ◽  
Spin Fields ◽  
Higher Spin Fields

Abstract We construct an unfolded system for off-shell fields of arbitrary integer spin in 4d anti-de Sitter space. To this end we couple an on-shell system, encoding Fronsdal equations, to external Fronsdal currents for which we find an unfolded formulation. We present a reduction of the Fronsdal current system which brings it to the unfolded Fierz-Pauli system describing massive fields of arbitrary integer spin. Reformulating off-shell higher-spin system as the set of Schwinger–Dyson equations we compute propagators of higher-spin fields in the de Donder gauge directly from the unfolded equations. We discover operators that significantly simplify this computation, allowing a straightforward extraction of wave equations from an unfolded system.

scholarly journals Superstrings in thermal anti-de Sitter space

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Sujay K. Ashok ◽  
Jan Troost
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Isometry Group ◽  
Three Dimensional ◽  
Open Interval ◽  
Energy Calculation ◽  
De Sitter ◽  
Half Open Interval ◽  
Sitter Spacetime ◽  
Discrete Representations

Abstract We revisit the calculation of the thermal free energy for string theory in three-dimensional anti-de Sitter spacetime with Neveu-Schwarz-Neveu-Schwarz flux. The path integral calculation is exploited to confirm the off-shell Hilbert space and we find that the Casimir of the discrete representations of the isometry group takes values in a half-open interval. We extend the free energy calculation to the case of superstrings, calculate the boundary toroidal twisted partition function in the Ramond-Ramond sector, and prove lower bounds on the boundary conformal dimension from the bulk perspective. We classify Ramond-Ramond ground states and construct their second quantized partition function. The partition function exhibits intriguing modular properties.

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 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.

Sign in / Sign up

Export Citation Format

Share Document