Investigations into light-front interactions for massless fields (I): non-constructibility of higher spin quartic amplitudes

It is shown that an action inspired from a BF and Chern–Simons model, based on the AdS4 isometry group SO(3,2), with the inclusion of a Higgs potential term, furnishes the MacDowell–Mansouri–Chamseddine–West action for gravity, with a Gauss–Bonnet and cosmological constant term. The AdS4 space is a natural vacuum of the theory. Using Vasiliev's procedure to construct higher spin massless fields in AdS spaces and a suitable star product, we discuss the preliminary steps to construct the corresponding higher-spin action in AdS4 space representing the higher spin extension of this model. Brief remarks on noncommutative gravity are made.

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AdS3/AdS2 degression of massless particles

Journal of High Energy Physics ◽

10.1007/jhep09(2021)198 ◽

2021 ◽

Vol 2021 (9) ◽

Author(s):

Konstantin Alkalaev ◽

Alexander Yan

Keyword(s):

Massless Particle ◽

Higher Dimensions ◽

Two Dimensions ◽

Spin Representation ◽

Theoretical Terms ◽

Finite Spectrum ◽

Branching Rules ◽

Higher Spin ◽

Massless Fields ◽

Kaluza Klein

Abstract We study a 3d/2d dimensional degression which is a Kaluza-Klein type mechanism in AdS3 space foliated into AdS2 hypersurfaces. It is shown that an AdS3 massless particle of spin s = 1, 2, …, ∞ degresses into a couple of AdS2 particles of equal energies E = s. Note that the Kaluza-Klein spectra in higher dimensions are always infinite. To formulate the AdS3/AdS2 degression we consider branching rules for AdS3 isometry algebra o(2,2) representations decomposed with respect to AdS2 isometry algebra o(1,2). We find that a given o(2,2) higher-spin representation lying on the unitary bound (i.e. massless) decomposes into two equal o(1,2) modules. In the field-theoretical terms, this phenomenon is demonstrated for spin-2 and spin-3 free massless fields. The truncation to a finite spectrum can be seen by using particular mode expansions, (partial) diagonalizations, and identities specific to two dimensions.

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A compendium of sphere path integrals

Journal of High Energy Physics ◽

10.1007/jhep12(2021)213 ◽

2021 ◽

Vol 2021 (12) ◽

Author(s):

Y.T. Albert Law

Keyword(s):

Standard Procedure ◽

Path Integrals ◽

Symmetric Tensor ◽

Arbitrary Spin ◽

Tensor Fields ◽

Arbitrary Integer ◽

Integer Spin ◽

Higher Spin ◽

Detailed Derivation ◽

Massless Fields

Abstract We study the manifestly covariant and local 1-loop path integrals on Sd+1 for general massive, shift-symmetric and (partially) massless totally symmetric tensor fields of arbitrary spin s ≥ 0 in any dimensions d ≥ 2. After reviewing the cases of massless fields with spin s = 1, 2, we provide a detailed derivation for path integrals of massless fields of arbitrary integer spins s ≥ 1. Following the standard procedure of Wick-rotating the negative conformal modes, we find a higher spin analog of Polchinski’s phase for any integer spin s ≥ 2. The derivations for low-spin (s = 0, 1, 2) massive, shift-symmetric and partially massless fields are also carried out explicitly. Finally, we provide general prescriptions for general massive and shift-symmetric fields of arbitrary integer spins and partially massless fields of arbitrary integer spins and depths.

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Double copy structure of parity-violating CFT correlators

Journal of High Energy Physics ◽

10.1007/jhep07(2021)033 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Sachin Jain ◽

Renjan Rajan John ◽

Abhishek Mehta ◽

Amin A. Nizami ◽

Adithya Suresh

Keyword(s):

Flat Space ◽

Field Theories ◽

Tree Level ◽

Conformal Field Theories ◽

Conformal Field ◽

Higher Spin ◽

Space Limit ◽

Double Copy ◽

Conserved Currents ◽

Massless Fields

Abstract We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators. Splitting up the CFT correlator into two parts — called homogeneous and non-homogeneous — we show that double copy relations exist for each part separately. We arrive at similar conclusions regarding double copy structures using tree-level correlators of massless fields in dS4. We also discuss the flat space limit of these correlators. We further extend the double copy analysis to correlators involving higher-spin conserved currents, which suggests that the spin-s current correlator can be thought of as s copies of the spin one current correlator.

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Unitarizable massless fields of higher order and higher spin

Journal of Mathematical Physics ◽

10.1063/1.529270 ◽

1991 ◽

Vol 32 (6) ◽

pp. 1586-1590

Author(s):

W. F. Heidenreich

Keyword(s):

Higher Order ◽

Higher Spin ◽

Massless 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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