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

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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Actions for self-dual Higher Spin Gravities

Journal of High Energy Physics ◽

10.1007/jhep08(2021)076 ◽

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.

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Frame-like Lagrangians and presymplectic AKSZ-type sigma models

International Journal of Modern Physics A ◽

10.1142/s0217751x14501036 ◽

2014 ◽

Vol 29 (18) ◽

pp. 1450103 ◽

Cited By ~ 2

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.

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