Constraining conformal field theories with a slightly broken higher spin symmetry

By J. Maldacena, A. Zhiboedov. 2012

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We consider three-dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large-N limit in the sense that the operators separate into single trace and multitrace and obey the usual large-N factorization properties. We assume that the spectrum of single trace operators is similar to the one that one obtains in the Vasiliev theories. Namely the only single trace operators are the higher spin currents plus an additional scalar. The anomalous dimensions of the higher spin currents are of the order 1/N. Using the slightly broken higher spin symmetry, we constrain the three-point functions of the theories to a leading order in N. We show that there are two families of solutions. One family can be realized as a theory of N fermions with an O(N) Chern–Simons gauge field, the other as an N bosons plus the Chern–Simons gauge field. The family of solutions is parametrized by the 't Hooft coupling. At special parity preserving points, we obtain the critical O(N) models: the Wilson–Fisher one and the Gross–Neveu one. Our analysis also fixes the on-shell three-point functions of Vasiliev's theory on AdS4 or dS4.

Subfields: Nuclear and High Energy Physics, Political Science and International Relations

View Paper: https://www.semanticscholar.org/paper/b3aead21ac5bf2840f0a94024660d10ab8c1d5f0

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Citations in the corpus

Universality of long-distance AdS physics from the CFT bootstrap (2014, background): “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.”
Implications of conformal invariance in momentum space (2013, background): “A complete analysis of all such 3-point functions, and in general dimension, was carried out in [3, 4]; for a sample of more recent work on this topic see also [5–11].”
Holographic geometry of entanglement renormalization in quantum field theories (2012, background): “It is also useful to note that the gravity dual of O(N) scalar field theory is given by the higher spin gravity [50] as has been recently studied actively [51, 52, 53, 54, 55].”
Higher spins & strings (2014, background): “Another interesting direction concerns the case of AdS3 × S3 × K3, for which one may try to identify a suitable higher spin theory and relate it to the symmetric 15It is also intriguing that extended chiral W-algebras have recently shown up in the description of supersymmetric sectors of N = 2 and N”
Black holes in three dimensional higher spin gravity: a review (2012, methodology): “Furthermore the large amount of symmetry makes it feasible to perform calculations of AdS/CFT correlators in the black hole background, which can help to address many basic questions of black hole physics, such as the formation and evaporation and the information paradox.”
The higher spin/vector model duality (2012, methodology): “The dependence of the three-point function on θ0 agrees with the general form constrained by slightly broken higher spin symmetry [19].”
The bootstrap program for boundary CFTd (2012, background): “Perhaps the constraints of sligthly broken higher-spin symmetry [30, 31] could help in organizing the information contained in (2.”
Baryons, monopoles and dualities in Chern-Simons-matter theories (2015, background): “duality, and by the classification of theories with slightly broken high-spin symmetries [7, 8].”
Correlators of large N fermionic Chern-Simons vector models (2012, methodology): “of the critical model, which is a “quasi-bosonic” theory in the language of [3].”
Minimal model holography (2012, background): “As we have mentioned before, μ = 1 corresponds to a free boson theory, and thus the fact that hs[μ] with μ 6= 1 is not a genuine symmetry of the theory at finite c is the two-dimensional incarnation of the result of [94, 95].”
Bounding the space of holographic CFTs with chaos (2016, methodology): “We use this term in the original sense of [78]: these are CFTs with some large parameter Ñ ∼ c and a coupling λ̃, with higher spin symmetry breaking of the schematic form”
The thermal free energy in large N Chern-Simons-matter theories (2012, methodology): “However, as shown in [8], these correlators are all determined by the almost-conserved highspin symmetry, and it would be nice to be able to test the duality by properties that are not determined purely by this symmetry.”
AdS description of induced higher-spin gauge theory (2013, methodology): “dualities [21–29], and we will make further use of them in this paper.”