Partition functions of holographic minimal models

By M. Gaberdiel, Rajesh Gopakumar, Thomas Hartman, S. Raju. 2011

220 citations recorded by the source corpus.

The partition function of the $ {\mathcal{W}_N} $ minimal model CFT is computed in the large N ’t Hooft limit and compared to the spectrum of the proposed holographic dual, a 3d higher spin gravity theory coupled to massive scalar fields. At finite N, the CFT contains additional light states that are not visible in the perturbative gravity theory. We carefully define the large N limit, and give evidence that, at N = ∞, the additional states become null and decouple from all correlation functions. The surviving states are shown to match precisely (for all values of the ’t Hooft coupling) with the spectrum of the higher spin gravity theory. The agreement between bulk and boundary is partially explained by symmetry considerations involving the conjectured equivalence between the $ {\mathcal{W}_N} $ algebra in the large N limit and the higher spin algebra of the Vasiliev theory.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1dcd84e4ee5e5307a38a132cc492e736e5538609

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Citations in the corpus

Black holes in three dimensional higher spin gravity: a review (2012, methodology): “The calculation of the 1-loop contribution to the bulk partition function utilizing heat-kernel methods [52,53] agrees with the large N limit of the CFT partition function of the coset theories (1.”
Partition functions of higher spin black holes and their CFT duals (2011, background): “Evidence for this proposal, based on symmetries, RG flows, and the perturbative spectrum, is discussed in [13,14,15,16].”
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 ”
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].”
Conical defects in higher spin theories (2011, methodology): “For further developments on this conjecture, including generalizations in various directions, see [11, 12, 13, 14, 15, 16, 17, 18, 19, 20].”
Large \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 4 holography (2013, unknown): “Fourthly, when the dual ﬁeld theories are studied on a non-simply connected space (such as S 1 for the 2d CFTs and a Riemann surface of genus > 1 for the 3d CFTs) there is an eﬀective continuum of light states that appears in the large N limit [5, 9, 10].”
Minimal model holography (2012, methodology): “Taking the large-N limit and evaluating on the Weyl vector, we can define the specialized Schur functions PR(q) ≡ χu(∞) R (zi) (zi = qi− 1 2 ), (147) P+ R (q) ≡ q+ λ 2 PR(q), where B(R) is the number of boxes in the Young diagram R; explicit formulae for the Schur functions can be found in the appen”
Higher spins & strings (2014, methodology): “Thus the perturbative part of the Vasiliev theory is captured by the subsector of the CFT [45, 46, 47] H = ⊕”
Scalar fields and three-point functions in D = 3 higher spin gravity (2011, background): “A separate question, not addressed here, is whether this is indeed true of the minimal model CFTs in the ’t Hooft limit; evidence in favor appears in [21,22,25].”
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.”
Chern–Simons theory with vector fermion matter (2011, background): “Its duality with higher spin gauge theories and in particular Vasiliev’s system in AdS3 are further explored in [13–17].”
Triality in minimal model holography (2012, methodology): “In fact, heuristic considerations [8] based on generalised level-rank dualities for coset CFTs [16, 17] suggest such a relation; this will be reviewed at the beginning of section 2 below.”
Spacetime geometry in higher spin gravity (2011, background): “This conjecture has been investigated further in [34,35,36,37].”
Higher spin gravity with matter in AdS3 and its CFT dual (2011, methodology): “It is shown in [34] that the descendants of the light states give rise to bound states of the basic primaries, while the light states themselves become null in the infinite N limit.”
Bounding the space of holographic CFTs with chaos (2016, background): “[52,66–69]); and W-algebras do appear widely in CFT.”