AdS Taub-Nut Space and the O(N) Vector Model on a Squashed 3-Sphere

In this note, motivated by the Klebanov-Polyakov conjecture we investigate the strongly coupled O(N) vector model at large $N$ on a squashed three-sphere and its holographic relation to bulk gravity on asymptotically locally $AdS_4$ spaces. We present analytical results for the action of the field theory as the squashing parameter $\alpha\to-1$, when the boundary becomes effectively one dimensional. The dual bulk geometry is AdS-Taub-NUT space in the corresponding limit. In this limit we solve the theory exactly and show that the action of the strongly coupled boundary theory scales as $\ln(1+\alpha)/ (1+\alpha)^2$. This result is remarkably close to the $-1/(1+\alpha)^2$ scaling of the Einstein gravity action for AdS-Taub-NUT space. These results explain the numerical agreement presented in hep-th/0503238, and the soft logarithmic departure is interpreted as a prediction for the contribution due to higher spin fields in the bulk $AdS_4$ geometry.Comment: 11 pages, 3 figures. References adde

dS/CFT correspondence on a brane

We study branes moving in an AdS Schwarzschild black hole background. When the brane tension exceeds a critical value, the induced metric on the brane is of FRW type and asymptotically de Sitter. We discuss the relevance of such configurations to dS/CFT correspondence. When the black hole mass reaches a critical value that depends on the brane tension, the brane interpolates in the infinite past and future between a dS space and a finite space of zero Hubble constant. This corresponds to a cosmological evolution without a Big Bang or a Big Crunch. Moreover, the central charge of the CFT dual to the dS brane enters the Cardy-Verlinde formula that gives the entropy of the thermal CFT dual to the bulk AdS black hole.Comment: 15 pages, 1 figure, v2 references adde

Evaluating the AdS dual of the critical O(N) vector model

We argue that the AdS dual of the three dimensional critical O(N) vector model can be evaluated using the Legendre transform that relates the generating functionals of the free UV and the interacting IR fixed points of the boundary theory. As an example, we use our proposal to evaluate the minimal bulk action of the scalar field that it is dual to the spin-zero ``current'' of the O(N) vector model. We find that the cubic bulk self interaction coupling vanishes. We briefly discuss the implications of our results for higher spin theories and comment on the bulk-boundary duality for subleading N.Comment: 17 pages, 1 figure, v2 references added, JHEP versio

Entropy bounds, monotonicity properties and scaling in CFTs

We study the ratio of the entropy to the total energy in conformal field theories at finite temperature. For the free field realizations of {\cal N}=4 super Yang-Mills theory in D=4 and the (2,0) tensor multiplet in D=6, the ratio is bounded from above. The corresponding bounds are less stringent than the recently proposed Verlinde bound. We show that entropy bounds arise generically in CFTs in connection to monotonicity properties with respect to temperature changes of a generalized C-function. For strongly coupled CFTs with AdS duals, we show that the ratio obeys the Verlinde bound even in the presence of rotation. For such CFTs, we point out an intriguing resemblance in their thermodynamic formulas with the corresponding ones of two-dimensional CFTs. We show that simple scaling forms for the free energy and entropy of CFTs with AdS duals reproduce the thermodynamical properties of (D+1)-dimensional AdS black holes.Comment: 19p, LaTeX, v2 minor clarifications and added references, v3 version to appear in NP

Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings

The correspondences proposed previously between higher spin gauge theories and free singleton field theories were recently extended into a more complete picture by Klebanov and Polyakov in the case of the minimal bosonic theory in D=4 to include the strongly coupled fixed point of the 3d O(N) vector model. Here we propose an N=1 supersymmetric version of this picture. We also elaborate on the role of parity in constraining the bulk interactions, and in distinguishing two minimal bosonic models obtained as two different consistent truncations of the minimal N=1 model that retain the scalar or the pseudo-scalar field. We refer to these models as the Type A and Type B models, respectively, and conjecture that the latter is holographically dual to the 3d Gross-Neveu model. In the case of the Type A model, we show the vanishing of the three-scalar amplitude with regular boundary conditions. This agrees with the O(N) vector model computation of Petkou, thereby providing a non-trivial test of the Klebanov-Polyakov conjecture.Comment: 30p

Holography of the N=1 Higher-Spin Theory on AdS4

We argue that the N=1 higher-spin theory on AdS4 is holographically dual to the N=1 supersymmetric critical O(N) vector model in three dimensions. This appears to be a special form of the AdS/CFT correspondence in which both regular and irregular bulk modes have similar roles and their interplay leads simultaneously to both the free and the interacting phases of the boundary theory. We study various boundary conditions that correspond to boundary deformations connecting, for large-N, the free and interacting boundary theories. We point out the importance of parity in this holography and elucidate the Higgs mechanism responsible for the breaking of higher-spin symmetry for subleading N.Comment: 19 page

Product CFTs, gravitational cloning, massive gravitons and the space of gravitational duals

The question of graviton cloning in the context of the bulk/boundary correspondence is considered. It is shown that multi-graviton theories can be obtained from products of large-N CFTs. No more than one interacting massless graviton is possible. There can be however, many interacting massive gravitons. This is achieved by coupling CFTs via multi-trace marginal or relevant perturbations. The geometrical structure of the gravitational duals of such theories is that of product manifolds with their boundaries identified. The calculational formalism is described and the interpretation of such theories is discussed.Comment: Latex, 25 pages. (v2) Minor corrections and references adde

The O(N) model on a squashed S^3 and the Klebanov-Polyakov correspondence

We solve the O(N) vector model at large N on a squashed three-sphere with a conformal mass term. Using the Klebanov-Polyakov version of the AdS_4/CFT_3 correspondence we match various aspects of the strongly coupled theory with the physics of the bulk AdS Taub-NUT and AdS Taub-Bolt geometries. Remarkably, we find that the field theory reproduces the behaviour of the bulk free energy as a function of the squashing parameter. The O(N) model is realised in a symmetric phase for all finite values of the coupling and squashing parameter, including when the boundary scalar curvature is negative.Comment: 1+27 pages. 6 figures. LaTeX. References adde

On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image

We explore the conjectured duality between the critical O(N) vector model and minimal bosonic massless higher spin (HS) theory in AdS. In the boundary free theory, the conformal partial wave expansion (CPWE) of the four-point function of the scalar singlet bilinear is reorganized to make it explicitly crossing-symmetric and closed in the singlet sector, dual to the bulk HS gauge fields. We are able to analytically establish the factorized form of the fusion coefficients as well as the two-point function coefficient of the HS currents. We insist in directly computing the free correlators from bulk graphs with the unconventional branch. The three-point function of the scalar bilinear turns out to be an "extremal" one at d=3. The four-leg bulk exchange graph can be precisely related to the CPWs of the boundary dual scalar and its shadow. The flow in the IR by Legendre transforming at leading 1/N, following the pattern of double-trace deformations, and the assumption of degeneracy of the hologram lead to the CPWE of the scalar four-point function at IR. Here we confirm some previous results, obtained from more involved computations of skeleton graphs, as well as extend some of them from d=3 to generic dimension 2<d<4.Comment: 22 pages, 5 figure