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 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 ANTI-DE SITTER SPACE, THERMAL PHASE TRANSITION AND CONFINEMENT IN GAUGE THEORIES

2001 ◽  
Vol 16 (16) ◽  
pp. 2747-2769 ◽  
Author(s):  
EDWARD WITTEN
Keyword(s):  
Gauge Theories ◽  
De Sitter Space ◽  
Spontaneous Breaking ◽  
De Sitter ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field ◽  
Classical Geometry ◽  
Large N ◽  
Quantum Phenomena

The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of [Formula: see text] super-Yang–Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale "holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.

scholarly journals On     1, 2, 4 higher spin gauge theories in four dimensions

2002 ◽  
Vol 19 (23) ◽  
pp. 6175-6196 ◽  
Author(s):  
J Engquist ◽  
E Sezgin ◽  
P Sundell
Keyword(s):  
Gauge Theories ◽  
Four Dimensions ◽  
Higher Spin

scholarly journals A connection between linearized Gauss–Bonnet gravity and classical electrodynamics II: Complete dual formulation

2021 ◽  
pp. 2150030
Author(s):  
Mark Robert Baker
Keyword(s):  
Field Strength ◽  
Gauge Theories ◽  
Equations Of Motion ◽  
Classical Electrodynamics ◽  
Necessary Condition ◽  
Property A ◽  
Gauge Invariant ◽  
Bonnet Gravity ◽  
Dual Formulation ◽  
Higher Spin

In a recent publication, a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with [Formula: see text] order of derivatives and [Formula: see text] rank of tensor potential. This procedure was then used to show that unique models follow for each order, namely classical electrodynamics for [Formula: see text] and linearized Gauss–Bonnet gravity for [Formula: see text]. In this paper, the nature of the connection between these two well-explored physical models is further investigated by means of an additional common property; a complete dual formulation. First, we give a review of Gauss–Bonnet gravity and the dual formulation of classical electrodynamics. The dual formulation of linearized Gauss–Bonnet gravity is then developed. It is shown that the dual formulation of linearized Gauss–Bonnet gravity is analogous to the homogenous half of Maxwell’s theory; both have equations of motion corresponding to the (second) Bianchi identity, built from the dual form of their respective field strength tensors. In order to have a dually symmetric counterpart analogous to the nonhomogenous half of Maxwell’s theory, the first invariant derived from the procedure in [Formula: see text] can be introduced. The complete gauge invariance of a model with respect to Noether’s first theorem, and not just the equation of motion, is a necessary condition for this dual formulation. We show that this result can be generalized to the higher spin gauge theories, where the spin-[Formula: see text] curvature tensors for all [Formula: see text] are the field strength tensors for each [Formula: see text]. These completely gauge invariant models correspond to the Maxwell-like higher spin gauge theories whose equations of motion have been well explored in the literature.

scholarly journals A pure connection formulation with real fields for gravity

2020 ◽  
pp. 2050114
Author(s):  
J. E. Rosales-Quintero
Keyword(s):  
Lie Algebra ◽  
Lagrange Multipliers ◽  
General Class ◽  
Equations Of Motion ◽  
Conformally Flat ◽  
Einstein Manifolds ◽  
De Sitter ◽  
Killing Form ◽  
Dual Approach ◽  
Four Dimensions

We study an [Formula: see text] pure connection formulation in four dimensions for real-valued fields, inspired by the Capovilla, Dell and Jacobson complex self-dual approach. By considering the CMPR BF action, also, taking into account a more general class of the Cartan–Killing form for the Lie algebra [Formula: see text] and by refining the structure of the Lagrange multipliers, we integrate out the metric variables in order to obtain the pure connection action. Once we have obtained this action, we impose certain restrictions on the Lagrange multipliers, in such a way that the equations of motion led us to a family of torsionless conformally flat Einstein manifolds, parametrized by two numbers. Finally, we show that, by a suitable choice of parameters, self-dual spaces (Anti-) de Sitter can be obtained.

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 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 Generalised superconformal higher-spin multiplets

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Sergei M. Kuzenko ◽  
Michael Ponds ◽  
Emmanouil S. N. Raptakis
Keyword(s):  
Gauge Fields ◽  
Conformally Flat ◽  
Component Level ◽  
Gauge Invariant ◽  
Weyl Invariance ◽  
Maximal Depth ◽  
Higher Spin ◽  
Bach Flat

Abstract 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.

TOPLESS ELECTROWEAK MODEL AS ANOMALOUS GAUGE THEORY

1993 ◽  
Vol 08 (18) ◽  
pp. 1639-1647 ◽  
Author(s):  
T. FUJIWARA ◽  
S. KITAKADO
Keyword(s):  
Gauge Theory ◽  
Top Quark ◽  
General Framework ◽  
Gauge Theories ◽  
Higgs Bosons ◽  
Electroweak Theory ◽  
Gauge Invariant ◽  
Four Dimensions ◽  
The Standard Model ◽  
Electroweak Model

General framework for quantizing anomalous gauge theories in four dimensions is applied to the description of electroweak theory that lacks the top quark. Auxiliary fields introduced to recover the gauge invariance substitute for the Higgs bosons of the standard model. The gauge invariant action contains the anomaly canceling Wess-Zumino-Witten term.

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
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