Conical Defects in Higher Spin Theories

We study conical defect geometries in the SL(N) Chern-Simons formulation of higher spin gauge theories in AdS_3. We argue that (for N\geq 4) there are special values of the deficit angle for which these geometries are actually smooth configurations of the underlying theory. We also exhibit a gauge in which these geometries can be viewed as wormholes interpolating between two distinct asymptotically AdS_3 spacetimes. Remarkably, the spectrum of smooth SL(N,C) solutions, after an appropriate analytic continuation, exactly matches that of the so-called "light primaries" in the minimal model W_N CFTs at finite N. This gives a candidate bulk interpretation of the latter states in the holographic duality proposed in [1].Comment: 38 page

The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models

Starting from SO(N) current algebra, we construct two lowest primary higher spin-4 Casimir operators which are quartic in spin-1 fields. For N is odd, one of them corresponds to the current in the WB_{\frac{N-1}{2}} minimal model. For N is even, the other corresponds to the current in the WD_{\frac{N}{2}} minimal model. These primary higher spin currents, the generators of wedge subalgebra, are obtained from the operator product expansion of fermionic (or bosonic) primary spin-N/2 field with itself in each minimal model respectively. We obtain, indirectly, the three-point functions with two real scalars, in the large N 't Hooft limit, for all values of the 't Hooft coupling which should be dual to the three-point functions in the higher spin AdS_3 gravity with matter.Comment: 65 pages; present the main results only and to appear in JHEP where one can see the Appendi

Higher Spin Black Holes from CFT

Higher spin gravity in three dimensions has explicit black holes solutions, carrying higher spin charge. We compute the free energy of a charged black hole from the holographic dual, a 2d CFT with extended conformal symmetry, and find exact agreement with the bulk thermodynamics. In the CFT, higher spin corrections to the free energy can be calculated at high temperature from correlation functions of W-algebra currents.Comment: 24 pages; v2 reference adde

Triality in Minimal Model Holography

The non-linear W_{\infty}[\mu] symmetry algebra underlies the duality between the W_N minimal model CFTs and the hs[\mu] higher spin theory on AdS_3. It is shown how the structure of this symmetry algebra at the quantum level, i.e. for finite central charge, can be determined completely. The resulting algebra exhibits an exact equivalence (a`triality') between three (generically) distinct values of the parameter \mu. This explains, among other things, the agreement of symmetries between the W_N minimal models and the bulk higher spin theory. We also study the consequences of this triality for some of the simplest W_{\infty}[\mu] representations, thereby clarifying the analytic continuation between the`light states' of the minimal models and conical defect solutions in the bulk. These considerations also lead us to propose that one of the two scalar fields in the bulk actually has a non-perturbative origin.Comment: 29 pages; v2. Typos correcte

The Coset Spin-4 Casimir Operator and Its Three-Point Functions with Scalars

We find the GKO coset construction of the dimension 4 Casimir operator that contains the quartic WZW currents contracted with completely symmetric SU(N) invariant tensors of ranks 4, 3, and 2. The requirements, that the operator product expansion with the diagonal current is regular and it should be primary under the coset Virasoro generator of dimension 2, fix all the coefficients in spin-4 current, up to two unknown coefficients. The operator product expansion of coset primary spin-3 field with itself fixes them completely. We compute the three-point functions with scalars for all values of the 't Hooft coupling in the large N limit. At fixed 't Hooft coupling, these three-point functions are dual to that found by Chang and Yin recently in the undeformed AdS_3 bulk theory (higher spin gravity with matter).Comment: 65 pages; the ambiguity for the two coefficient functions is clarified and the abstract, the introduction, the subsection 3.4 and the conclusion are improved and to appear in JHE

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The Large N 't Hooft Limit of Kazama-Suzuki Model

We consider N=2 Kazama-Suzuki model on CP^N=SU(N+1)/SU(N)xU(1). It is known that the N=2 current algebra for the supersymmetric WZW model, at level k, is a nonlinear algebra. The N=2 W_3 algebra corresponding to N=2 was recovered from the generalized GKO coset construction previously. For N=4, we construct one of the higher spin currents, in N=2 W_5 algebra, with spins (2, 5/2, 5/2, 3). The self-coupling constant in the operator product expansion of this current and itself depends on N as well as k explicitly. We also observe a new higher spin primary current of spins (3, 7/2, 7/2, 4). From the behaviors of N=2, 4 cases, we expect the operator product expansion of the lowest higher spin current and itself in N=2 W_{N+1} algebra. By taking the large (N, k) limit on the various operator product expansions in components, we reproduce, at the linear order, the corresponding operator product expansions in N=2 classical W_{\infty}^{cl}[\lambda] algebra which is the asymptotic symmetry of the higher spin AdS_3 supergravity found recently.Comment: 44 pages; the two typos in the first paragraph of page 23 corrected and to appear in JHE

Unitarity Bounds in AdS_3 Higher Spin Gravity

We study SL(N,R) Chern-Simons gauge theories in three dimensions. The choice of the embedding of SL(2,R) in SL(N,R), together with asymptotic boundary conditions, defines a theory of higher spin gravity. Each inequivalent embedding leads to a different asymptotic symmetry group, which we map to an OPE structure at the boundary. A simple inspection of these algebras indicates that only the W_N algebra constructed using the principal embedding could admit a unitary representation for large values of the central charge.Comment: 1+23 pages, Version 3 Appendix B revise

Symmetries of Holographic Super-Minimal Models

We compute the asymptotic symmetry of the higher-spin supergravity theory in AdS_3 and obtain an infinite-dimensional non-linear superalgebra, which we call the super-W_infinity[lambda] algebra. According to the recently proposed supersymmetric duality between higher-spin supergravity in an AdS_3 background and the 't Hooft limit of the N=2 CP^n Kazama-Suzuki model on the boundary, this symmetry algebra should agree with the 't Hooft limit of the chiral algebra of the CFT, SW_n. We provide two nontrivial checks of the duality. By comparing the algebras, we explicitly match the lowest-spin commutation relations in the super-W_infinity[lambda] with the corresponding commutation relations in the 't Hooft limit on the CFT side. We also consider the degenerate representations of the two algebras and find that the spectra of the chiral primary fields are identical.Comment: 33 pages, references added, some errors corrected, discussions about the truncation of the shs[lambda] algebra and reobtaining the original shs[lambda] algebra from the super-W_infinity[lambda] algebra adde

Limits of minimal models and continuous orbifolds

The lambda=0 't Hooft limit of the 2d W_N minimal models is shown to be equivalent to the singlet sector of a free boson theory, thus paralleling exactly the structure of the free theory in the Klebanov-Polyakov proposal. In 2d, the singlet sector does not describe a consistent theory by itself since the corresponding partition function is not modular invariant. However, it can be interpreted as the untwisted sector of a continuous orbifold, and this point of view suggests that it can be made consistent by adding in the appropriate twisted sectors. We show that these twisted sectors account for the `light states' that were not included in the original 't Hooft limit. We also show that, for the Virasoro minimal models (N=2), the twisted sector of our orbifold agrees precisely with the limit theory of Runkel & Watts. In particular, this implies that our construction satisfies crossing symmetry.Comment: 33 pages; v2: minor improvements and references added, published versio