Off-shell higher-spin fields in AdS4 and external currents

Abstract We construct an unfolded system for off-shell fields of arbitrary integer spin in 4d anti-de Sitter space. To this end we couple an on-shell system, encoding Fronsdal equations, to external Fronsdal currents for which we find an unfolded formulation. We present a reduction of the Fronsdal current system which brings it to the unfolded Fierz-Pauli system describing massive fields of arbitrary integer spin. Reformulating off-shell higher-spin system as the set of Schwinger–Dyson equations we compute propagators of higher-spin fields in the de Donder gauge directly from the unfolded equations. We discover operators that significantly simplify this computation, allowing a straightforward extraction of wave equations from an unfolded system.

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Lagrangian Formulation of Free Arbitrary N-Extended Massless Higher Spin Supermultiplets in 4D AdS Space

Symmetry ◽

10.3390/sym12122052 ◽

2020 ◽

Vol 12 (12) ◽

pp. 2052

Author(s):

Ioseph L. Buchbinder ◽

Timofey V. Snegirev

Keyword(s):

Explicit Form ◽

De Sitter Space ◽

Lagrangian Formulation ◽

De Sitter ◽

Integer Spin ◽

Half Integer ◽

Higher Spin ◽

Spin Fields ◽

Higher Spin Fields

We derived the component Lagrangian for the free N-extended on-shell massless higher spin supermultiplets in four-dimensional anti-de Sitter space. The construction was based on the frame-like description of massless integer and half-integer higher spin fields. The massless supermultiplets were formulated for N≤4k, where k is a maximal integer or half-integer spin in the multiplet. The supertransformations that leave the Lagrangian invariant were found in explicit form and it was shown that their algebra is closed on-shell.

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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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Relativistic Wave Equations Including Higher Spin Fields

Encyclopedia of Mathematical Physics ◽

10.1016/b0-12-512666-2/00161-9 ◽

2006 ◽

pp. 391-398

Author(s):

R. Illge ◽

V. Wünsch

Keyword(s):

Wave Equations ◽

Relativistic Wave Equations ◽

Relativistic Wave ◽

Higher Spin ◽

Spin Fields ◽

Higher Spin Fields

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The σ− Cohomology Analysis for Symmetric Higher-Spin Fields

Symmetry ◽

10.3390/sym13081498 ◽

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.

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