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.
We generalize the Goddard-Kent-Olive (GKO) coset construction to the dimension 5/2 operator for $ \hat{so} (5) $ and compute the fourth order Casimir invariant in the coset model $\hat{SO} (5)_{1} \times \hat{SO} (5)_{m} / \hat{SO} (5)_{1+m} $ with the generic unitary minimal $ c < 5/2 $ series that can be viewed as perturbations of the $ m \rightarrow \infty $ limit, which has been investigated previously in the realization of $ c= 5/2 $ free fermion model.
We compute the operator product expansion (OPE) between the spin-4 current and itself in the WD_4 coset minimal model with SO(8) current algebra. The right hand side of this OPE contains the spin-6 Casimir current which is also a generator of WD_4 coset minimal model. Based on this N=8 result, we generalize the above OPE for the general N(in the WD_{N/2} coset minimal model) by using two N-generalized coupling constants initiated by Hornfeck sometime ago: the simplest OPE for the lowest higher spin currents. We also analyze the similar OPE in the WB_3(and WB_{(N-1)/2}) coset minimal model with…
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 …
We consider a general class of asymptotically locally AdS_5 solutions of minimal gauged supergravity, that are dual to superconformal field theories on curved backgrounds S^1 x M_3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S^1 x R^4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory BPS relation between charges.
In the N=1 supersymmetric coset minimal model based on (B_N^{(1)} \oplus D_N^{(1)}, D_N^{(1)}) at level (k,1) studied recently, the standard N=1 super stress tensor of spins (3/2,2) is reviewed. By considering the stress tensor in the coset (B_N^{(1)}, D_N^{(1)}) at level k, the higher spin-2' Casimir current was obtained previously. By acting the above spin-3/2 current on the higher spin-2' Casimir current, its superpartner, the higher spin-5/2 current, can be generated and combined as the first higher spin supercurrent with spins (2', 5/2). By calculating the operator product expansions (OPE…
By calculating the second-order pole in the operator product expansion (OPE) between the spin-3 Casimir operator and the spin-4 Casimir operator known previously, the spin-5 Casimir operator is obtained in the coset model based on (A_{N-1}^{(1)} \oplus A_{N-1}^{(1)}, A_{N-1}^{(1)}) at level (k,1). This spin-5 Casimir operator consisted of the quintic, quartic (with one derivative) and cubic (with two derivatives) WZW currents contracted with SU(N) invariant tensors. The three-point functions with two scalars for all values of 't Hooft coupling in the large N limit were obtained by analyzing th…
We study the holographic duality between the M x M matrix extension of Vasiliev higher spin theories on AdS3 and the large N limit of SU(N+M)/SU(N) x U(1) type cosets. We present a simplified proof for the agreement of the spectra and clarify the relation between this duality and the version in which the cosets are replaced by Kazama-Suzuki models of Grassmannian type.
We show that in the Randall-Sundrum model the Casimir energy of bulk gauge fields (or any of their supersymmetric relatives) has contributions that depend logarithmically on the radion. These contributions satisfactorily stabilize the radion, generating a large hierarchy of scales without fine-tuning. The logarithmic behaviour can be understood, in a 4D holographic description, as the running of gauge couplings with the infrared cut-off scale.
We compute the Casimir energy of the photon field in a de Sitter space and find it to be proportional to the size of the horizon, the same form of the holographic dark energy. We suggest to make metamaterials to mimic de Sitter space in laboratory and measure the predicted Casimir energy.
M/string theory on noncompact, negatively curved, cosets which generalize $AdS_{D+1}=SO(D,2)/SO(D,1)$ is considered. Holographic descriptions in terms of a conformal field theory on the boundary of the spacetime are proposed. Examples include $SU(2,1)/U(2)$, which is a Euclidean signature (4,0) space with no supersymmetry, and $SO(2,2)/SO(2)$ and $SO(3,2)/SO(3)$, which are Lorentzian signature (4,1) and (6,1) spaces with eight supersymmetries. Qualitatively new features arise due to the degenerate nature of the conformal boundary metric.
In this paper, we investigate Casimir effect, Weyl anomaly and displacement operator for boundary conformal field theory in general dimensions. We find universal relations between them. In particular, they are all determined by the central charge of boundary conformal field theory. We verify these relations by studying free BCFTs and holographic BCFTs. As a byproduct, we obtain the holographic two point function of stress tensor when the bulk boundary is perpendicular to the AdS boundary.
Within the context of top-down holography, we study a one-parameter family of regular background solutions of maximal gauged supergravity in seven dimensions, dimensionally reduced on a 2-torus. The dual, four-dimensional confining field theory realises the global (spontaneous as well as explicit) symmetry breaking pattern SO(5)->SO(4). We compute the complete mass spectrum for the fluctuations of the 128 bosonic degrees of freedom of the five-dimensional gravity theory, which correspond to scalar, pseudoscalar, vector, axial-vector, and tensor bound states of the dual field theory, and includ…
We build a novel time-like coset sigma-model describing type-II superstring theory in a charged rotating black-brane background that interpolates between a locally $AdS_3$ in the IR and a linear-dilaton geometry in the UV. This allows one to perform a systematic study of holography in non-AdS backgrounds which are smoothly connected to $AdS_3$. We construct massless closed string states vertex operators in the NS-NS sector, calculate the corresponding two-point correlation functions, and discuss holographic interpretation of our results from 4+1 dimensional boundary field theory point of view.…
It has been believed for a long time that the tensionless limit of superstring theory can be described by a higher spin gauge theory. Recently, a concrete realization of this idea was proposed via 3d Aharony-Bergman-Jafferis (ABJ) theory with the help of holographic duality. In this note we review our work on finding a similar relation involving 2d coset type models. We start by proposing and examining holographic dualities between 3d higher spin gauge theories with matrix valued fields and the large N limit of 2d coset type models. After that we discuss possible relations to superstring theor…
We study conformal field theories in two dimensions separated by domain walls, which preserve at least one Virasoro algebra. We develop tools to study such domain walls, extending and clarifying the concept of `folding' discussed in the condensed-matter literature. We analyze the conditions for unbroken supersymmetry, and discuss the holographic duals in AdS3 when they exist. One of the interesting observables is the Casimir energy between a wall and an anti-wall. When these separate free scalar field theories with different target-space radii, the Casimir energy is given by the dilogarithm fu…
We present the holographic object which computes the five-point global conformal block in arbitrary dimensions for external and exchanged scalar operators. This object is interpreted as a weighted sum over infinitely many five-point geodesic bulk diagrams. These five-point geodesic bulk diagrams provide a generalization of their previously studied four-point counterparts. We prove our claim by showing that the aforementioned sum over geodesic bulk diagrams is the appropriate eigenfunction of the conformal Casimir operator with the right boundary conditions. This result rests on crucial inspira…
We reassess employing the holographic technique to the description of 4D minimal composite Higgs model with $SO(5)\to SO(4)$ global symmetry breaking pattern. The particular 5D bottom-up holographic treatment is inspired by previous work in the context of QCD and it allows to study spin one and spin zero resonances. The resulting spectrum consists of the states transforming under the unbroken $SO(4)$ subgroup and those with quantum numbers in the $SO(5)/SO(4)$ coset. The spin one states are arranged in linear radial trajectories, and the states from the broken subgroup are generally heavier. T…
This study reconsidered the N=1 supersymmetric extension of the W_3 algebra which was studied previously. This extension consists of seven higher spin supercurrents (fourteen higher spin currents in the components) as well as the N=1 stress energy tensor of spins (3/2, 2). Thus far, the complete expressions for the higher spin currents have not been derived. This paper constructs them explicitly in both the c=4 eight free fermion model and the supersymmetric coset model based on (A_2^{(1)} \oplus A_2^{(1)}, A_2^{(1)})$ at level (3,k). By acting with the above spin-3/2 current on the higher spi…
Using trace anomalies, we determine the vacuum stress tensors of arbitrary even dimensional conformal field theories in Weyl flat backgrounds. We demonstrate a simple relation between the Casimir energy on the real line times a sphere and the type A anomaly coefficient. This relation generalizes earlier results in two and four dimensions. These field theory results for the Casimir are shown to be consistent with holographic predictions in two, four, and six dimensions.
Recently, a 2d coset model with N=3 superconformal symmetry was proposed to be holographic dual to a higher spin supergravity on AdS_3 and the relation to superstring theory was discussed. However, away from the tensionless limit, there is no higher spin symmetry and the higher spin states are massive. In this paper, we examine the deformations of the coset model which preserve N=3 superconformal symmetry, but break generic higher spin symmetry. We focus on double-trace type deformations which are dual to changes of boundary conditions for the bulk matter fields. In the bulk theory, the symmet…
We propose a holographic duality between a higher spin AdS_3 gravity with so(p) extended supersymmetry and a large N limit of a 2-dimensional Grassmannian-like model with a specific critical level k=N and a non-diagonal modular invariant. As evidence, we show the match of one-loop partition functions. Moreover, we construct symmetry generators of the coset model for low spins which are dual to gauge fields in the supergravity. Further, we discuss a possible relation to superstring theory by noticing an N=3 supersymmetry of critical level model at finite k,N. In particular, we examine BPS state…
The results of the paper of Verlinde [hep-th/0008140], discussing the holographic principle in a radiation dominated universe, are extended when allowing the cosmic fluid to possess a bulk viscosity. This corresponds to a non-conformally invariant theory. The generalization of the Cardy-Verlinde entropy formula to the case of a viscous universe seems from a formal point of view to be possible, although we question on physical grounds some elements in this kind of theory, especially the manner in which the Casimir energy is evaluated. Our discussion suggests that for non-conformally invariant t…
The low energy field theory for N type IIA D4-branes at strong 't Hooft coupling, wrapped on a circle with antiperiodic boundary conditions for fermions, is known to have a vacuum energy which depends on the $θ$ angle for the gauge fields, and which is a multivalued function of this angle. This gives a field-theoretic realization of "axion monodromy" for a nondynamical axion. We construct the supergravity solution dual to the field theory in the metastable state which is the adiabatic continuation of the vacuum to large values of $θ$. We compute the energy of this state and show that it initia…
We prove a generalised Flato-Fronsdal theorem for higher-order, scalar and spinor, singletons. In the resulting infinite tower of bulk higher-spin fields, we point out the occurrence of partially-massless fields of all depths. This leads us to conjecture a holographic duality between a higher-spin gravity theory around $AdS_{d+1}$ with the aforementioned spectrum of fields, and a free $CFT_d$ of fundamental (higher-order) scalar and spinor singletons. As a first check of this conjecture, we find that the total Casimir energy vanishes at one loop.
We study a 5D bottom-up holographic model that is expected to describe the dynamics of the minimal composite Higgs model characterized by a $SO(5)\to SO(4)$ global symmetry breaking pattern. We assume that the fundamental degrees of freedom are scalars transforming under some representation of $SO(5)$ and subject to some unspecified strong interactions. The holographic description presented here is inspired by previous studies performed in the context of QCD and it allows for the consideration of spin one and spin zero resonances. The resulting spectrum leads in a natural way to a variety of r…
The 3d spin-3 gravity theory is holographically dual to a 2d ${\cal W}_3$-extended CFT. In a large-c limit the symmetry algebra of the CFT reduces to $SU(1,2) \times SU(1,2)$. On the ground of symmetry the dual bulk space-time will be given by an 8d group manifold $SU(1,2)$. Hence we need to introduce five extra coordinates in addition to three ordinary ones. The 3d space-time is a 3d hyper-surface $Σ$ embedded at constant values of the extra variables. Operators in the CFT at the boundary of $Σ$ are expressed in terms of ${\cal W}$ descendants of the operators at the boundary of $Σ_0$, where …
In this work we study the well known contact term, which is the key element in resolving the so-called $U(1)_A$ problem in QCD. We study this term using the dual Holographic Description. We argue that in the dual picture the contact term is saturated by the D2 branes which can be interpreted as the tunnelling events in Minkowski space-time. We quote a number of direct lattice results supporting this identification. We also argue that the contact term receives a Casimir -like correction $\sim (\Lqcd R)^{-1}$ rather than naively expected $\exp(-\Lqcd R)$ when the Minkowski space-time ${\cal R}_{…
We study quantum fields on an arbitrary, rigid background with boundary. We derive the action for a scalar in the holographic basis that separates the boundary and bulk degrees of freedom. A relation between Dirichlet and Neumann propagators valid for any background is obtained from this holographic action. As a simple application, we derive an exact formula for the flux of bulk modes emitted from the boundary in a warped background. We also derive a formula for the Casimir pressure on a $(d-1)$-brane depending only on the boundary-to-bulk propagators, and apply it in AdS. Turning on couplings…
We suggest that the principle of holographic duality can be extended beyond conformal invariance and AdS isometry. Such an extension is based on a special relation between functional determinants of the operators acting in the bulk and on its boundary, provided that the boundary operator represents the inverse propagators of the theory induced on the boundary by the Dirichlet boundary value problem from the bulk spacetime. This relation holds for operators of general spin-tensor structure on generic manifolds with boundaries irrespective of their background geometry and conformal invariance, a…
We give a general account of nonlocal symmetries in symmetric space models and their relation to the AdS/CFT correspondence. In particular, we study a master symmetry which generates the spectral parameter and acts as a level-raising operator on the classical Yangian generators. The master symmetry extends to an infinite tower of symmetries with nonlocal Casimir elements as associated conserved charges. We discuss the algebraic properties of these symmetries and establish their role in explaining the recently observed one-parameter deformation of holographic Wilson loops. Finally, we provide a…
