scholarly journals Frame-like Lagrangians and presymplectic AKSZ-type sigma models

2014 ◽  
Vol 29 (18) ◽  
pp. 1450103 ◽  
Author(s):  
Konstantin Alkalaev ◽  
Maxim Grigoriev
Keyword(s):  
Degrees Of Freedom ◽  
Scalar Potential ◽  
Hamiltonian Formalism ◽  
Target Space ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
Finite Dimensional ◽  
Higher Spin ◽  
Spin Fields ◽  
Parametrized Systems

We study supergeometric structures underlying frame-like Lagrangians. We show that for the theory in n space–time dimensions both the frame-like Lagrangian and its gauge symmetries are encoded in the target supermanifold equipped with the odd vector field, the closed two-form of ghost degree n-1, and the scalar potential of ghost degree n. These structures satisfy a set of compatibility conditions ensuring the gauge invariance of the theory. The Lagrangian and the gauge symmetries have the same structures as those of AKSZ sigma model so that frame-like formulation can be seen as its presymplectic generalization. In contrast to the conventional AKSZ model, the generalization allows to describe systems with local degrees of freedom in terms of finite-dimensional target space. We argue that the proposed frame-like approach is directly related de Donder–Weyl polymomentum Hamiltonian formalism. Along with the standard field-theoretical examples like Einstein–Yang–Mills theory, we consider free higher spin fields, multi-frame gravity and parametrized systems. In particular, we propose the frame-like action for free totally symmetric massless fields that involves all higher spin connections on an equal footing.

scholarly journals A note on higher-order vertices of higher-spin fields in flat and (A)dS space

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Euihun Joung ◽  
Massimo Taronna
Keyword(s):  
Arbitrary Number ◽  
Flat Space ◽  
Higher Order ◽  
Yang Mills ◽  
Homogeneous Solutions ◽  
Gauge Symmetries ◽  
Higher Spin ◽  
Spin Fields ◽  
Higher Spin Fields

Abstract In this work we classify (homogeneous) solutions to the Noether procedure in (A)dS for an arbitrary number of external legs and in general dimensions, analysing also the corresponding deformations of gauge symmetries. This builds upon the corresponding flat space classification [1], which we review and give its relation with the (A)dS result presented here. The role of dimensional dependent identities is studied in detail, which we find do not lead to new solutions for couplings involving more than three fields. For spins one and two our formalism recovers the Yang-Mills and Gravity examples.

scholarly journals Actions for self-dual Higher Spin Gravities

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Kirill Krasnov ◽  
Evgeny Skvortsov ◽  
Tung Tran
Keyword(s):  
Higher Spin Gravity ◽  
Gravitational Interaction ◽  
De Sitter Space ◽  
Twistor Theory ◽  
Covariant Form ◽  
De Sitter ◽  
Yang Mills ◽  
Higher Spin ◽  
Spin Fields ◽  
Higher Spin Fields

Abstract Higher Spin Gravities are scarce, but covariant actions for them are even scarcer. We construct covariant actions for contractions of Chiral Higher Spin Gravity that represent higher spin extensions of self-dual Yang-Mills and self-dual Gravity theories. The actions give examples of complete higher spin theories both in flat and (anti)-de Sitter spaces that feature gauge and gravitational interactions. The actions are based on a new description of higher spin fields, whose origin can be traced to early works on twistor theory. The new description simplifies the structure of interactions. In particular, we find a covariant form of the minimal gravitational interaction for higher spin fields both in flat and anti-de Sitter space, which resolves some of the puzzles in the literature.

scholarly journals Dirac's Footsteps and Supersymmetry

2004 ◽  
Vol 19 (supp01) ◽  
pp. 89-97 ◽  
Author(s):  
Pierre Ramond
Keyword(s):  
Dirac Equation ◽  
Light Cone ◽  
Theoretical Interpretation ◽  
Compact Structure ◽  
Four Dimensions ◽  
Yang Mills ◽  
Higher Spin ◽  
Spin Fields ◽  
Front Form ◽  
M Theory

One hundred years after its creator's birth, the Dirac equation stands as the cornerstone of XXth Century physics. But it is much more, as it carries the seeds of supersymmetry. Dirac also invented the light-cone, or "front form" dynamics, which plays a crucial role in string theory and in elucidating the finiteness of N=4 Yang-Mills theory. The light-cone structure of eleven-dimensional supergravity (N=8 supergravity in four dimensions) suggests a group-theoretical interpretation of its divergences. We speculate they could be compensated by an infinite number of triplets of massless higher spin fields, each obeying a Dirac-like equation associated with the coset F4/SO(9). The divergences are proportional to the trace over a non-compact structure containing the compact form of F4. Its nature is still unknown, but it could show the way to M-theory.

A SUPERCONFORMAL THEORY OF MASSLESS HIGHER SPIN FIELDS IN D=2+1

1989 ◽  
Vol 04 (08) ◽  
pp. 731-744 ◽  
Author(s):  
E.S. FRADKIN ◽  
V. YA. LINETSKY
Keyword(s):  
Space Time ◽  
Superconformal Algebra ◽  
Conformal Supergravity ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Higher Spin ◽  
Spin Fields ◽  
Chern Simons ◽  
Supergravity Action ◽  
Higher Spin Fields

We construct a superconformal theory of higher spin fields in a space-time of dimension D=2+1. The construction relies on the infinite-dimensional superalgebra shsc (N/3) with the superconformal algebra OSp (N/4) as a maximal finite-dimensional subalgebra. The invariant Chern-Simons action for the higher spin superconformal theory is an extension of the usual conformal supergravity action for particles with maximal spin two.

HYPERPARTICLES, TWISTORS AND ANY SPINS

2012 ◽  
Vol 09 (06) ◽  
pp. 1261012
Author(s):  
DMITRI SOROKIN
Keyword(s):  
Degrees Of Freedom ◽  
Higher Spin ◽  
Spin Fields ◽  
Relativistic Particles ◽  
Higher Spin Fields

In this contribution I would like to review some topics in which Jerzy Lukierski has been one of the main players and contributed over decades with many interesting and important results. We shall consider various ways in which relativistic particles can be endowed with spin degrees of freedom with the use of twistor-like variables and supersymmetrization, which upon quantization lead either to higher-spin fields (in D > 3) or to anions (in D = 3).

scholarly journals Light-front quantization with the light cone gauge

2016 ◽  
Vol 94 (5) ◽  
pp. 511-516
Author(s):  
D.G.C. McKeon ◽  
Chenguang Zhao
Keyword(s):  
Light Cone ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Light Front ◽  
Target Space ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Dirac Brackets ◽  
Light Front Quantization ◽  
Gauge Conditions

The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first-class constraints that arise and the resulting Dirac brackets are found. These gauge conditions are not used to eliminate degrees of freedom from the action prior to applying the Dirac constraint procedure. This approach is illustrated by considering Yang–Mills theory and the superparticle in a 2+1-dimensional target space.

scholarly journals From Center-Vortex Ensembles to the Confining Flux Tube

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 253
Author(s):  
David R. Junior ◽  
Luis E. Oxman ◽  
Gustavo M. Simões
Keyword(s):  
Degrees Of Freedom ◽  
String Tension ◽  
Effective Field ◽  
Scaling Properties ◽  
Flux Tubes ◽  
Topological Solitons ◽  
Yang Mills ◽  
Center Vortex ◽  
Asymptotic Scaling ◽  
The Continuum

In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

scholarly journals Scrambling in Yang-Mills

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert de Mello Koch ◽  
Eunice Gandote ◽  
Augustine Larweh Mahu
Keyword(s):  
Relaxation Time ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Dilatation Operator ◽  
Super Yang Mills Theory

Abstract Acting on operators with a bare dimension ∆ ∼ N2 the dilatation operator of U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the graph while edges correspond to terms in the Hamiltonian. The graph has p ∼ N vertices. Using this Hamiltonian, we study scrambling and equilibration in the large N Yang-Mills theory. We characterize the typical graph and thus the typical Hamiltonian. For the typical graph, the dynamics leads to scrambling in a time consistent with the fast scrambling conjecture. Further, the system exhibits a notion of equilibration with a relaxation time, at weak coupling, given by t ∼ $$ \frac{\rho }{\lambda } $$ ρ λ with λ the ’t Hooft coupling.

scholarly journals Gauging the higher-spin-like symmetries by the Moyal product

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
M. Cvitan ◽  
P. Dominis Prester ◽  
S. Giaccari ◽  
M. Paulišić ◽  
I. Vuković
Keyword(s):  
Linear Connection ◽  
Covariant Formulation ◽  
Formal Similarity ◽  
Commutative Field ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Higher Derivative ◽  
Novel Approach ◽  
Emergent Geometry ◽  
Higher Spin

Abstract We analyze a novel approach to gauging rigid higher derivative (higher spin) symmetries of free relativistic actions defined on flat spacetime, building on the formalism originally developed by Bonora et al. and Bekaert et al. in their studies of linear coupling of matter fields to an infinite tower of higher spin fields. The off-shell definition is based on fields defined on a 2d-dimensional master space equipped with a symplectic structure, where the infinite dimensional Lie algebra of gauge transformations is given by the Moyal commutator. Using this algebra we construct well-defined weakly non-local actions, both in the gauge and the matter sector, by mimicking the Yang-Mills procedure. The theory allows for a description in terms of an infinite tower of higher spin spacetime fields only on-shell. Interestingly, Euclidean theory allows for such a description also off-shell. Owing to its formal similarity to non-commutative field theories, the formalism allows for the introduction of a covariant potential which plays the role of the generalised vielbein. This covariant formulation uncovers the existence of other phases and shows that the theory can be written in a matrix model form. The symmetries of the theory are analyzed and conserved currents are explicitly constructed. By studying the spin-2 sector we show that the emergent geometry is closely related to teleparallel geometry, in the sense that the induced linear connection is opposite to Weitzenböck’s.

Sign in / Sign up

Export Citation Format

Share Document