Constraining conformal field theories with a higher spin symmetry

By J. Maldacena, A. Zhiboedov. 2011

580 citations recorded by the source corpus.

We study the constraints imposed by the existence of a single higher spin conserved current on a three-dimensional conformal field theory (CFT). A single higher spin conserved current implies the existence of an infinite number of higher spin conserved currents. The correlation functions of the stress tensor and the conserved currents are then shown to be equal to those of a free field theory. Namely a theory of N free bosons or free fermions. This is an extension of the Coleman–Mandula theorem to CFT’s, which do not have a conventional S-matrix. We also briefly discuss the case where the higher spin symmetries are ‘slightly’ broken. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7b664eb6932286034f66d6c1a2d0b2325e500587

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Citations in the corpus

The higher spin/vector model duality (2012, background): “It was shown in [18] that a conformal field theory with exact higher spin symmetry must be a free theory.”
Universality of long-distance AdS physics from the CFT bootstrap (2014, methodology): “19) We have limited this sum to `m ≤ 2, because higher spin operators either possess twist greater than that of the energy-momentum tensor or couple [23, 62] as in a free field theory.”
Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory (2012, methodology): “. The HS symmetry of the correlators as well as the conservation of the currents are manifest. Therefore, the results of the paper can be also viewed as a complement to the MaldacenaZhiboedov theorem [2]. To be more precise, [2] classiﬁes all HS algebras together with their unitary irreducible repre”
Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions (2012, background): “Explicit expressions for these structures can be found in [35, 36, 23].”
TASI Lectures on the Conformal Bootstrap (2016, background): “nt: (134) Some important examples are global symmetry currents (‘= 1, = d 1) and the stress tensor (‘= 2, = d). For CFTs in d3, the presence of currents with spin ‘3 implies that the theory is free [34,35].dd 7.4. Only Primaries and Descendants With a positive-denite inner product, we can now prove ”
Chern Simons duality with a fundamental boson and fermion (2013, background): “vable’ in the large N limit. We now have explicit formulae for the spectrum of single sum operators, three point correlation functions and thermal partition functions for some of these theories – 1 – [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. These exact results have already led to the discovery o”
The thermal free energy in large N Chern-Simons-matter theories (2012, background): “• The approximate high-spin symmetry allows for an exact evaluation of all 2-point and 3-point functions of “single-trace” primary operators1, up to two (or three) parameters [7, 8].”
Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations (2015, background): “The Coleman-Mandula theorem [54] (and its conformal version [55]) states that unitary local CFTs can only have compact reductive Lie algebras as internal (flavor) symmetries, and so we expect physical CB deformations should have only Weyl group symmetries.”
Vertex operator algebras, Higgs branches, and modular differential equations (2017, background): “The latter condition holds in any interacting CFT [58].”
Bootstrapping the O(N ) vector models (2013, methodology): “Previously, bootstrap ideas have been applied to the O(N) vector models in the 1/N expansion, for example in work by Lang and Rühl [22–27], Petkou [28, 29], and more recently Maldacena and Zhiboedov [30, 31].”
Exact correlators of BPS Operators from the 3d superconformal bootstrap (2014, background): “This multiplet contains higher-spin conserved currents, and therefore can only appear in the free theory [70].”
Refined stable pair invariants for E-, M- and [p, q]-strings (2013, background): “So it is a quite concrete proposal for the spectrum for a conformal higher spin theory of the type recently analyzed in [58, 59].”
Infinite Chiral Symmetry in Four Dimensions (2013, background): “If any such multiplets are present, the SCFT must contain a decoupled free sector [29].”
ABJ triality: from higher spin fields to strings (2012, background): “s that it would be interesting, purely within ﬁeld theory, to study ABJ theory in a power expansion in M N but nonperturbatively in λ. At M N = 0 this would require a generalization of the results of [8] and [9] to the supersymmetric theory. It may then be possible to systematically correct this sol”
Multiplets of superconformal symmetry in diverse dimensions (2016, methodology): “metric, traceless stress tensor with = d, respectively. In d 3 dimensions, conserved higher-spin currents with s3 are only believed to exist in CFTs that contain a locally free, decoupled subsector [42,44]. In order to dene a notion of spin for operators in more general Lorentz representations, we e”
AdS description of induced higher-spin gauge theory (2013, background): “The theory obtained by gauging the whole set of HS currents also does not obey the theorem of [24], being a higher spin gauge theory (in particular including gravity), while [24] assumes a CFT with global HS symmetries and corresponding exactly conserved currents.”