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Register a new userTest of the local form of higher-spin equations via AdS/CFT
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The local form of higher-spin equations found recently to the second order [1] is shown to properly reproduce the anticipated $AdS/CFT$ correlators for appropriate boundary conditions. It is argued that consistent $AdS/CFT$ holography for the parity-broken boundary models needs a nontrivial modification of the bosonic truncation of the original higher-spin theory with the doubled number of fields, as well as a nonlinear deformation of the boundary conditions in the higher orders.
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We aim at formulating a higher-spin gravity theory around AdS$_2$ relevant for holography. As a first step, we investigate its kinematics by identifying the low-dimensional cousins of the standard higher-dimensional structures in higher-spin gravity such as the singleton, the higher-spin symmetry algebra, the higher-rank gauge and matter fields, etc. In particular, the higher-spin algebra is given here by $hs[lambda]$ and parameterized by a real parameter $lambda$. The singleton is defined to be a Verma module of the AdS$_2$ isometry subalgebra $so(2,1) subset hs[lambda]$ with conformal weight $Delta = frac{1pmlambda}{2},$. On the one hand, the spectrum of local modes is determined by the Flato-Fronsdal theorem for the tensor product of two such singletons. It is given by an infinite tower of massive scalar fields in AdS$_2$ with ascending masses expressed in terms of $lambda$. On the other hand, the higher-spin fields arising through the gauging of $hs[lambda]$ algebra do not propagate local degrees of freedom. Our analysis of the spectrum suggests that AdS$_2$ higher-spin gravity is a theory of an infinite collection of massive scalars with fine-tuned masses, interacting with infinitely many topological gauge fields. Finally, we discuss the holographic CFT$_1$ duals of the kinematical structures identified in the bulk.
We find a simple relation between a free higher spin field partition function on thermal quotient of AdS(d+1) and the partition function of the associated d-dimensional conformal higher spin field on thermal quotient of AdS(d). Starting with a conformal higher spin field defined on AdS(d) one may also associate to it another conformal field in d-1 dimensions, thus iterating AdS/CFT. We observe that in the case of d=4 this iteration leads to a trivial 3d higher spin conformal theory with parity-even non-local action: it describes zero total number of dynamical degrees of freedom and the corresponding partition function on thermal AdS(3) is equal to 1.
The extension of nonlinear higher-spin equations in d=4 proposed in [arXiv:1504.07289] for the construction of invariant functional is shown to respect local Lorentz symmetry. The equations are rewritten in a manifestly Lorentz covariant form resulting from some Stueckelberg-like field transformation. We also show that the two field-independent central terms entering higher-spin equations which are not entirely fixed by the consistency alone get fixed unambiguously by the requirement of Lorentz symmetry. One of the important advantages of the proposed approach demonstrated in the paper is the remarkable simplification of the perturbative analysis.
We exploit the AdS/CFT correspondence to investigate thermalization in an N=2 strongly coupled gauge theory including massless fundamental matter (quark). More precisely, we consider the response of a zero temperature state of the gauge theory under variation of an external electric field leading to a time-dependent current. The holographic dual of the above set-up is given by introducing a time-dependent electric field on the probe D7-brane embedded in an AdS_5 X S^5 background. In the dual gravity theory, due to a time-dependent electric field an apparent horizon forms on the brane which, according to AdS/CFT dictionary, is the counterpart of the thermalization process in the gauge theory. We classify different functions for time-dependent electric field and study their effect on the apparent horizon formation. In the case of pulse functions where the electric field varies from zero to zero, apart from non-equilibrium phase, we observe that two apparent horizons form on the brane. On the gauge theory side, it means that the state of the gauge theory experiences two different temperatures during the time evolution.
With a view to understanding extended-BMS symmetries in the framework of the $AdS_4/CFT_3$ correspondence, asymptotically AdS geometries are constructed with null impulsive shockwaves involving a discontinuity in superrotation parameters. The holographic dual is proposed to be a two-dimensional Euclidean defect conformal field localized on a particular timeslice in a three-dimensional conformal field theory on de Sitter spacetime. The defect conformal field theory generates a natural action of the Virasoro algebra. The large radius of curvature limit $elltoinfty$ yields spacetimes with nontrivial extended-BMS charges.
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