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Register a new userHolography and the Polyakov action
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In two dimensional conformal field theory the generating functional for correlators of the stress-energy tensor is given by the non-local Polyakov action associated with the background geometry. We study this functional holographically by calculating the regularized on-shell action of asymptotically AdS gravity in three dimensions, associated with a specified (but arbitrary) boundary metric. This procedure is simplified by making use of the Chern-Simons formulation, and a corresponding first-order expansion of the bulk dreibein, rather than the metric expansion of Fefferman and Graham. The dependence of the resulting functional on local moduli of the boundary metric agrees precisely with the Polyakov action, in accord with the AdS/CFT correspondence. We also verify the consistency of this result with regard to the nontrivial transformation properties of bulk solutions under Brown-Henneaux diffeomorphisms.
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In this work we present a closed form expression for Polyakov blocks in Mellin space for arbitrary spin and scaling dimensions. We provide a prescription to fix the contact term ambiguity uniquely by reducing the problem to that of fixing the contact term ambiguity at the level of cyclic exchange amplitudes -- defining cyclic Polyakov blocks -- in terms of which any fully crossing symmetric correlator can be decomposed. We also give another, equivalent, prescription which does not rely on a decomposition into cyclic amplitudes and we underline the relation between cyclic amplitudes and dispersion relations in Mellin space. We extract the OPE data of double-twist operators in the direct channel expansion of the cyclic Polyakov blocks using and extending the analysis of cite{Sleight:2018epi,Sleight:2018ryu} to include contributions that are non-analytic in spin. The relation between cyclic Polyakov blocks and analytic Bootstrap functionals is underlined.
We employ gauge-gravity duality to study the backreaction effect of 4-dimensional large-$N$ quantum field theories on constant-curvature backgrounds, and in particular de Sitter space-time. The field theories considered are holographic QFTs, dual to RG flows between UV and IR CFTs. We compute the holographic QFT contribution to the gravitational effective action for 4d Einstein manifold backgrounds. We find that for a given value of the cosmological constant $lambda$, there generically exist two backreacted constant-curvature solutions, as long as $lambda < lambda_{textrm{max}} sim M_p^2 / N^2$, otherwise no such solutions exist. Moreover, the backreaction effect interpolates between that of the UV and IR CFTs. We also find that, at finite cutoff, a holographic theory always reduces the bare cosmological constant, and this is the consequence of thermodynamic properties of the partition function of holographic QFTs on de Sitter.
We prove the Polyakov conjecture on the supertorus $(ST_2)$: we dermine an iterative solution at any order of the superconformal Ward identity and we show that this solution is resumed by the Wess-Zumino-Polyakov (WZP) action that describes the $(1,0)$ 2D-supergravity. The resolution of the superBeltrami equation for the Wess-Zumino (WZ) field is done by using on the one hand the Cauchy kernel defined on $ST_2$ and on the other hand, the formalism developed to get the general solution on the supercomplex plane. Hence, we determine the n-points Green functions from the (WZP) action expressed in terms of the (WZ) field.
We extend Boussos notion of a lightsheet - a surface where entropy can be defined in a way so that the entropy bound is satisfied - to more general surfaces. Intuitively these surfaces may be regarded as deformations of the Bousso choice; in general, these deformations will be timelike and so we refer to them as `timesheets. We show that a timesheet corresponds to a section of a certain twistor bundle over a given spacelike two-surface B. We further argue that increasing the entropy flux through a given region corresponds to increasing the volume of certain regions in twistor space. We further argue that in twistor space, it might be possible to give a purely topological characterization of a lightsheet, at least for suitably simple spacetimes.
On the basis of a number of Swampland conditions, we argue that the Hilbert space of baby universe states must be one-dimensional in a consistent theory of quantum gravity. This scenario may be interpreted as a type of Gausss law for entropy in quantum gravity, and provides a clean synthesis of the tension between Euclidean wormholes and a standard interpretation of the holographic dictionary, with no need for an ensemble. Our perspective relies crucially on the recently-proposed potential for quantum-mechanical gauge redundancies between states of the universe with different topologies. By an application of the state-operator correspondence, this proposal rules out the possibility of nontrivial, strictly well-defined bulk operators supported in a compact region. We further comment on the possible exceptions in $dleq 3$ for this hypothesis, and the role of an ensemble for holographic theories in low dimensions, such as JT gravity in $d = 2$ and possible cousins in $d=3$. We argue that these examples are incomplete physical theories that should be viewed as branes in a higher dimensional theory of quantum gravity, for which an ensemble plays no role.
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