Symmetries of holographic minimal models

By M. Gaberdiel, Thomas Hartman. 2011

321 citations recorded by the source corpus.

It was recently proposed that a large N limit of a family of minimal model CFTs is dual to a certain higher spin gravity theory in AdS3, where the ’t Hooft coupling constant of the CFT is related to a deformation parameter of the higher spin algebra. We identify the asymptotic symmetry algebra of the higher spin theory for generic ’t Hooft parameter, and show that it coincides with a family of $ \mathcal{W} $-algebras previously discovered in the context of the KP hierarchy. We furthermore demonstrate that this family of $ \mathcal{W} $-algebras controls the representation theory of the minimal model CFTs in the ’t Hooft limit. This provides a non-trivial consistency check of the proposal and explains part of the underlying mechanism.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f2c1d976b2ed15ede4681d1bd374e28da12b1b73

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Citations in the corpus

Towards integrability for AdS 3 / CFT 2 ?> (2014, background): “This provided a new approach to holograpic dualities, and lead to rapid developments [269–272]—see also ref.”
Towards metric-like higher spin gauge theories in three dimensions (2012, methodology): “It thus preserves the same amount of gauge symmetry as the sum of the linearized Einstein–Hilbert and Fronsdal actions.”
Thermodynamics of higher spin black holes in 3D (2012, background): “Spurred on by these developments another concrete proposal by Gaberdiel and Gopakumar [28] posits a duality between three dimensional higher spin theories and a WN minimal model CFT in a ’t Hooft-like large-N limit [29, 30, 31, 32].”
Higher spin AdS3 supergravity and its dual CFT (2011, methodology): “The theory is described by the 3d Chern-Simons theory based on two copies of sl(N) [7], and the asymptotic symmetry near the boundary is found to be the WN algebra [8, 9, 10, 11].”
Higher spin black holes from CFT (2012, background): “In the large N limit, the detailed microscopics of this proposal are supported by symmetries [14], the spectrum of primaries [15], and certain correlation functions [16, 17, 18, 19, 20]; at finite N some new ingredients may be required in the bulk (or perhaps can be found within the Vasiliev theory ”
Partition functions of higher spin black holes and their CFT duals (2011, methodology): “The spacetime interpretation and asymptotic symmetries of the SL(3,R) × SL(3,R) Chern-Simons theory were treated in detail in [29], following which [17,18] discovered smooth, asymptotically AdS3, black hole solutions with nonzero spin-3 charge and consistent thermodynamics.”
Partition functions of holographic minimal models (2011, methodology): “The bulk asymptotic symmetries form (two copies of) a larger algebra W∞[λ] that extends hs[λ] much like the Virasoro algebra extends sl(2) [16, 17, 22].”
Triality in minimal model holography (2012, methodology): “The particular cases studied in [3, 4] actually belong to a one-parameter family of higher spin theories whose symmetry algebras could be identified with W∞[μ] [5] (see also [6]).”
How higher-spin gravity surpasses the spin-two barrier (2010, unknown): “[142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152] and references therein.”
Asymptotically flat spacetimes in three-dimensional higher spin gravity (2013, background): “The asymptotically AdS3 conditions of [14, 15, 23, 24], that extend the ones of Brown and Henneaux to the case of higher spin fields, have been shown to possess an interesting vanishing cosmological constant limit.”
Black holes and singularity resolution in higher spin gravity (2011, background): “A full discussion of this prescription can be found in [34, 35, 36], and its implementation in higher spin theories in [37, 23, 38, 33].”
Higher spin black holes (2011, background): “Introduction Theories of gravity coupled to massless higher spin fields [1,2,3,4,5] have received increased attention in recent years due to their appearance within the AdS/CFT correspondence [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21].”
Conical defects in higher spin theories (2011, methodology): “The analysis in [11, 12] showed that in the ’t Hooft limit the spectrum of the WN minimal model instead falls into representations of W∞[λ], and hence the gauge group in the bulk is its wedge algebra, hs[λ].”
Higher spins & strings (2014, background): “We believe the AdS3/CFT2 case is particularly suited for this endeavour, because, unlike in higher dimensions, the higher spin symmetry group is enlarged here to aW∞ algebra [21, 22, 23] (generalising the enhancement to Virasoro discovered by Brown and Henneaux [24]).”
Bounding the space of holographic CFTs with chaos (2016, methodology): “This is the asymptotic symmetry algebra of hs[λ] Chern-Simons theory in AdS3, which also forms the gauge sector of 3D Vasiliev theory [39,40].”
Spacetime geometry in higher spin gravity (2011, background): “This conjecture has been investigated further in [34,35,36,37].”