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Symmetries of Holographic Minimal Models
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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 AdS_3, 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 W-algebras previously discovered in the context of the KP hierarchy. We furthermore demonstrate that this family of 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.
Forward citations
Cited by 3 Pith papers
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A universal W-algebra for N=4 super Yang-Mills
Using associativity constraints from OPE bootstrapping, the authors give evidence for a one-parameter W-algebra W∞^{s,s} that conjecturally truncates to the VOA of 4d N=4 SU(N) super Yang-Mills at c = -3(N²-1).
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On W-algebras and ODE/IM correspondence
The eigenvalues of quantum KdV-type charges in Virasoro, W3, and W4 algebras are computed from Bethe roots via WKB periods of Catalan curves, verified against direct CFT diagonalization.
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Higher-order chiral scalar from boundary reduction of 3d higher-spin gravity
Boundary reduction of 3d higher-spin Chern-Simons gravity yields covariant and gauge-fixed higher-derivative chiral-scalar actions for arbitrary spin s, with a factorized kinetic operator and special zero-mode backgrounds.
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