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.

UNCONSTRAINED HIGHER SPINS IN FOUR DIMENSIONS

2011 ◽  
Vol 08 (03) ◽  
pp. 511-556 ◽  
Author(s):  
GIUSEPPE BANDELLONI
Keyword(s):  
Equations Of Motion ◽  
Symmetric Tensor ◽  
Tensor Fields ◽  
Geometrical Meaning ◽  
Four Dimensions ◽  
Spin Field ◽  
Angular Momenta ◽  
Higher Spin ◽  
Spin Fields ◽  
The Right

The relativistic symmetric tensor fields are, in four dimensions, the right candidates to describe Higher Spin Fields. Their highest spin content is isolated with the aid of covariant conditions, discussed within a group theory framework, in which auxiliary fields remove the lower intrinsic angular momenta sectors. These conditions are embedded within a Lagrangian Quantum Field theory which describes an Higher Spin Field interacting with a Classical background. The model is invariant under a (B.R.S.) symmetric unconstrained tensor extension of the reparametrization symmetry, which include the Fang–Fronsdal algebra in a well defined limit. However, the symmetry setting reveals that the compensator field, which restore the Fang–Fronsdal symmetry of the free equations of motion, is in the existing in the framework and has a relevant geometrical meaning. The Ward identities coming from this symmetry are discussed. Our constraints give the result that the space of the invariant observables is restricted to the ones constructed with the Highest Spin Field content. The quantum extension of the symmetry reveals that no new anomaly is present. The role of the compensator field in this result is fundamental.

GENERATING FUNCTION FOR CUBIC INTERACTION VERTICES OF HIGHER SPIN FIELDS IN ANY DIMENSION

1993 ◽  
Vol 08 (25) ◽  
pp. 2413-2426 ◽  
Author(s):  
R. R. METSAEV
Keyword(s):  
Generating Function ◽  
Wide Class ◽  
Light Cone ◽  
Arbitrary Dimension ◽  
Space Time ◽  
Relativistic Dynamics ◽  
Higher Spin ◽  
Spin Fields ◽  
Higher Spin Fields

Using the light-cone formulation of relativistic dynamics we present a wide class of cubic interaction vertices for higher spin fields of any symmetry in arbitrary dimension of space-time. The solution is obtained in terms of generating function for interaction vertices.

scholarly journals A CFT distance conjecture

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Eric Perlmutter ◽  
Leonardo Rastelli ◽  
Cumrun Vafa ◽  
Irene Valenzuela
Keyword(s):  
Spin Symmetry ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Higher Spin ◽  
Spin Fields ◽  
Local Operators ◽  
Conformal Manifolds

Abstract We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

scholarly journals Supersymmetric HS Yang-Mills-like Models

Universe ◽  
2020 ◽  
Vol 6 (12) ◽  
pp. 245
Author(s):  
Loriano Bonora ◽  
Stefano Giaccari
Keyword(s):  
Four Dimensions ◽  
Yang Mills ◽  
Supersymmetric Version ◽  
Spin Fields

We introduce the supersymmetric version of YM-like theories with infinitely many spin fields in four dimensions. The construction is carried out via the superfield method. The surprising feature of these models is that they describe, in particular, gauge and gravity in a supersymmetric form, with no need for supergravity.

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 DEFORMED SUPERSYMMETRIC GAUGE THEORIES FROM THE FLUXTRAP BACKGROUND

2013 ◽  
Vol 28 (28) ◽  
pp. 1330044 ◽  
Author(s):  
DOMENICO ORLANDO ◽  
SUSANNE REFFERT
Keyword(s):  
String Theory ◽  
Gauge Theories ◽  
Recent Literature ◽  
Supersymmetric Gauge Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
M Theory ◽  
Super Yang Mills Theory ◽  
Gravity Duals

The fluxtrap background of string theory provides a transparent and algorithmic way of constructing supersymmetric gauge theories with both mass and Ω-type deformations in various dimensions. In this paper, we review a number of deformed supersymmetric gauge theories in two and four dimensions which can be obtained via the fluxtrap background from string or M-theory. Such theories, the most well-known being Ω-deformed super-Yang–Mills theory in four dimensions, have met with a lot of interest in the recent literature. The string theory treatment offers many new avenues of analysis and applications, such as for example the study of the gravity duals for deformed [Formula: see text] gauge theories.

scholarly journals Massless higher spin cubic vertices in flat four dimensional space

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
M. V. Khabarov ◽  
Yu. M. Zinoviev
Keyword(s):  
Cosmological Constant ◽  
Dimensional Space ◽  
Four Dimensions ◽  
Equal Footing ◽  
Higher Derivative ◽  
Higher Spin ◽  
Spin Fields ◽  
Higher Spin Fields ◽  
Taking Care

Abstract In this paper we construct a number of cubic interaction vertices for massless bosonic and fermionic higher spin fields in flat four dimensional space. First of all, we construct these cubic vertices in AdS4 space using a so-called Fradkin-Vasiliev approach, which works only for the non-zero cosmological constant. Then we consider a flat limit taking care on all the higher derivative terms which FV-approach generates. We restrict ourselves with the four dimensions because this allows us to use the frame-like multispinor formalism which greatly simplifies all calculations and provides a description for bosons and fermions on equal footing.

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 The σ− Cohomology Analysis for Symmetric Higher-Spin Fields

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1498
Author(s):  
Alexey S. Bychkov ◽  
Kirill A. Ushakov ◽  
Mikhail A. Vasiliev
Keyword(s):  
Minkowski Space ◽  
Dimensional Case ◽  
Arbitrary Integer ◽  
Complete Proof ◽  
Four Dimensions ◽  
Integer Spin ◽  
Half Integer ◽  
Higher Spin ◽  
Spin Fields ◽  
Massless Fields

In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer spin in any dimension and arbitrary integer or half-integer spin in four dimensions. This is achieved by calculation of the respective σ− cohomology both in the tensor language in Minkowski space of any dimension and in terms of spinors in AdS4. In the d-dimensional case Hp(σ−) is computed for any p and interpretation of Hp(σ−) is given both for the original Fronsdal system and for the associated systems of higher form fields.

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.

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