scholarly journals Conformal geometry and (super)conformal higher-spin gauge theories

2019 ◽  
Vol 2019 (5) ◽  
Author(s):  
Sergei M. Kuzenko ◽  
Michael Ponds
Keyword(s):  
Gauge Theories ◽  
Conformal Geometry ◽  
Higher Spin

scholarly journals BRST and Superfield Formalism—A Review

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 280
Author(s):  
Loriano Bonora ◽  
Rudra Prakash Malik
Keyword(s):  
Riemannian Geometry ◽  
Gauge Theories ◽  
Original Material ◽  
Comprehensive Description ◽  
Higher Spin ◽  
Gauge Anomalies

This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories, we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the superspace. We then illustrate the application to the description of consistent gauge anomalies and Wess–Zumino terms for which the formalism seems to be particularly tailor-made. The next subject covered is the higher spin YM-like theories and their anomalies. Finally, we show that the BRST superfield formalism applies as well to the N=1 super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well.

scholarly journals Real forms of extended Kac–Moody symmetries and higher spin gauge theories

2012 ◽  
Vol 44 (7) ◽  
pp. 1787-1834 ◽  
Author(s):  
Marc Henneaux ◽  
Axel Kleinschmidt ◽  
Hermann Nicolai
Keyword(s):  
Gauge Theories ◽  
Higher Spin ◽  
Real Forms

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 Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields

2018 ◽  
Vol 2018 (11) ◽  
Author(s):  
Marc Henneaux ◽  
Victor Lekeu ◽  
Amaury Leonard ◽  
Javier Matulich ◽  
Stefan Prohazka
Keyword(s):  
Conformal Geometry ◽  
Three Dimensional ◽  
Higher Spin ◽  
Spin Fields ◽  
Higher Spin Fields

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 On Killing tensors and cubic vertices in higher-spin gauge theories

2006 ◽  
Vol 54 (5-6) ◽  
pp. 282-290 ◽  
Author(s):  
X. Bekaert ◽  
N. Boulanger ◽  
S. Cnockaert ◽  
S. Leclercq
Keyword(s):  
Gauge Theories ◽  
Killing Tensors ◽  
Higher Spin

HIGHER SPIN ALGEBRAS AND QUANTIZATION ON THE SPHERE AND HYPERBOLOID

1991 ◽  
Vol 06 (07) ◽  
pp. 1115-1135 ◽  
Author(s):  
M.A. VASILIEV
Keyword(s):  
Gauge Theories ◽  
Dimensional Sphere ◽  
Infinite Dimensional ◽  
Matrix Algebras ◽  
Finite Dimensional ◽  
Continuous Parameter ◽  
Oscillator Type ◽  
Heisenberg Type ◽  
Higher Spin ◽  
Quantum Operators

The oscillator-type realization is proposed for the continuous set of infinite-dimensional algebras of quantum operators on the two-dimensional sphere and hyperboloid. This realization is typical for infinite-dimensional higher spin algebras related to higher spin gauge theories. It involves the Klein-type operator that emerges nontrivially in the Heisenberg-type commutation relations for the oscillators. The invariant trace and bilinear form are constructed. The latter is shown to degenerate for all odd-integer values of the continuous parameter ν, which parametrizes the class of algebras under investigation. The degeneration points are shown to correspond to ordinary finite-dimensional matrix algebras and superalgebras. Possible applications of these results to higher spin gauge theories are discussed. In particular, it is noted that the deformation parameter ν can be interpreted as a vacuum value of some auxiliary scalar field in an appropriate higher spin gauge theory.

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