Notes on higher-spin algebras: minimal representations and structure constants

Joung, Euihun; Mkrtchyan, Karapet

doi:10.1007/jhep05(2014)103

Cited by 81 publications

(158 citation statements)

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“…Originally, they were found as symmetries of conformally-invariant higher derivative equations k Φ(x) = 0 [12,14,15]. explicit structure constants [20,58]. It was also found in various contexts [19,20,59] that there are certain finite dimensional algebras that can be viewed as higher spin algebras, at least up to some point.…”

Section: Higher Spin Algebrasmentioning

confidence: 99%

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New conformal higher spin gravities in 3d

Grigoriev

Lovrekovic

Skvortsov

2020

J. High Energ. Phys.

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We propose a new class of conformal higher spin gravities in three dimensions, which extends the one by Pope and Townsend. The main new feature is that there are infinitely many examples of the new theories with a finite number of higher spin fields, much as in the massless case. The action has the Chern-Simons form for a higher spin extension of the conformal algebra. In general, the new theories contain Fradkin-Tseytlin fields with higher derivatives in the gauge transformations, which is reminiscent of partially-massless fields. A relation of the old and new theories to the parity anomaly is pointed out.

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Section: Higher Spin Algebrasmentioning

confidence: 99%

“…A large class of infinite-dimensional algebras is given by the symmetries of (higher-order) singletons, i.e. free CFT's of type q Φ = 0 and q−1 / ∂Ψ = 0, which were studied in [12,14,15,17,18,20,58,61]. These algebras are more difficult to work with, but the structure constants are explicitly available [20,58].…”

Section: C)mentioning

confidence: 99%

New conformal higher spin gravities in 3d

Grigoriev

Lovrekovic

Skvortsov

2020

J. High Energ. Phys.

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“…The appropriate concept that can be used to assess the "size" of an infinite dimensional representation is so-called Gelfand-Kirillov (GK) dimension [13]. Its proper definition is rather formal 4 , and for applications in physics, it would be enough to regard it as the number of continuous variables required for a given representation to be realized as a space of functions of these variables (see, e.g., [4]). With this concept, it is simple to see that the GK dimension of a tensor sum representation is the larger one among the GK dimensions of two representations, and the GK dimension of a tensor product representation is the sum of the two GK dimensions.…”

Section: Two Classes Of Examplesmentioning

confidence: 99%

“…This obstruction can be avoided if the massless spin two and PM spin two fields have relatively negative kinetic term signs. In such a case, the global symmetry becomes so (2,4) and in fact the resulting theory is nothing but the conformal gravity written in two-derivative form around a constant curvature background [31]. In the following sections, we shall attempt to fix the problem of PM gravity with the so(1, 5) (or, as we show, so(1, D + 1) in arbitrary dimensions D ≥ 4) global symmetry by enlarging the field content with additional fields or relaxing implicit assumptions of the no-go theorem, such as parity invariance and general covariance.…”

Section: Two Classes Of Examplesmentioning

confidence: 99%

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Looking for partially-massless gravity

Joung

Mkrtchyan

Poghosyan

2019

J. High Energ. Phys.

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We study the possibility for a unitary theory of partially-massless (PM) spintwo field interacting with Gravity in arbitrary dimensions. We show that the gauge and parity invariant interaction of PM spin two particles requires the inclusion of specific massive spin-two fields and leads to a reconstruction of Conformal Gravity, or multiple copies of the latter in even dimensions. By relaxing the parity invariance, we find a possibility of a unitary theory in four dimensions, but this theory cannot be constructed in the standard formulation, due to the absence of the parity-odd cubic vertex therein. Finally, by relaxing the general covariance, we show that a "non-geometric" coupling between massless and PM spin-two fields may lead to an alternative possibility of a unitary theory. We also clarify some aspects of interactions between massless, partially-massless and massive fields, and resolve disagreements in the literature. C PM Coupling to matter 38-i - 6. Postponing the justification of why 1 We will call PM gravity any unitary theory of gravity that involves PM spin-two field. 2 In [5], the authors require unitarity of the corresponding representation. We will use a looser form of admissibility condition, allowing non-unitary theories in general, even though our eventual goal is to understand the possibility of unitary theories. We will show, that even without the requirement of unitarity, the admissibility condition puts very strong restrictions on the space of possible theories.is composed of only gauge fields whose Killing tensors correspond to the generators of the symmetries. In this way, the finiteness of the dimension of the symmetry algebras implies the finiteness of the number of fields in the theories. In fact, there is no strong reason that there should be only gauge fields. Indeed, a good example is Vasiliev's higherspin gravity: the theory also requires a scalar field in the field content, which has no 3 By this definition, the depth is the number of derivatives in the gauge transformation of PM field, which is different from [12]. 4 See, e.g., Wikipedia: Gelfand-Kirillov dimension. 5 This does not rule out non-linear realisations of global symmetries. An interesting recent example was provided in [14], a special Galileon theory in (A)dS d+1 with extended symmetry (a real form of) sl d+2 , which is the k = 1 case of the PM HS algebras of [12] mentioned above. The no-go statement here refers to the possibility of gauging these algebras and realising their global action linearly on the fields.

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Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications

Sleight

Taronna

2018

Fortschritte der Physik

153

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We study conformal partial waves (CPWs) in Mellin space with totally symmetric external operators of arbitrary integer spin. The exchanged spin is arbitrary, and includes mixed symmetry and (partially)-conserved representations. In a basis of CPWs recently introduced in arXiv:1702.08619, we find a remarkable factorisation of the external spin dependence in their Mellin representation. This property allows a relatively straightforward study of inversion formulae to extract OPE data from the Mellin representation of spinning 4pt correlators and in particular, to extract closed-form expressions for crossing kernels of spinning CPWs in terms of the hypergeometric function 4 F 3 . We consider numerous examples involving both arbitrary internal and external spins, and for both leading and sub-leading twist operators. As an application, working in general d we extract new results for O(1/N) anomalous dimensions of double-trace operators induced by double-trace deformations constructed from single-trace operators of generic twist and integer spin. In particular, we extract the anomalous dimensions of double-trace operators [O J ] n,l with O J a single-trace operator of integer spin J. 1 See however [48] for recent analytic results for the scalar-fermion bootstrap. 2 The Mellin space approach to the conformal bootstrap was initiated in [32,33,57] for external scalar operators. 1 of 77) www.advancedsciencenews.com www.fp-journal.org In §5.2.1 we apply our formalism to spinning correlators in arbitrary space-time dimensions, which also requires to consider mixed symmetry CPWs and their crossing kernels -which we derive. In particular, using the methods of §3 we first extract mean-field theory OPE coefficients for leading twist double-trace operators [O J ] 0,l built from a spin-J single-trace operator O J and a scalar operator . Combining the latter with the results for crossing kernels, we then obtain the anomalous dimensions of the doubletrace operators [O J ] 0,l induced by the double-trace flow (1.1) with l = 0. (3 The basis itself was originally obtained in the context of simplifying the kinematic map between bulk cubic couplings and 3pt conformal structures, so our proposed framework also lends itself nicely to studies of bulk physics. 4 Some of such nested formulas recently appeared in the literature in a different CFT basis. [62] For external scalars, such formulas were originally given in [29].

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Notes on higher-spin algebras: minimal representations and structure constants

Cited by 81 publications

References 103 publications

New conformal higher spin gravities in 3d

New conformal higher spin gravities in 3d

Looking for partially-massless gravity

Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications

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