AdS/CFT correspondence

About: AdS/CFT correspondence is a research topic. Over the lifetime, 6660 publications have been published within this topic receiving 355520 citations.

Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT

Abstract: We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.

State-dependent bulk-boundary maps and black hole complementarity

Abstract: We provide a simple and explicit construction of local bulk operators that describe the interior of a black hole in the AdS/CFT correspondence. The existence of these operators is predicated on the assumption that the mapping of CFT operators to local bulk operators depends on the state of the CFT. We show that our construction leads to an exactly local effective field theory in the bulk. Barring the fact that their charge and energy can be measured at infinity, we show that the commutator of local operators inside and outside the black hole vanishes exactly, when evaluated within correlation functions of the CFT. Our construction leads to a natural resolution of the strong subadditivity paradox of Mathur and Almheiri et al. Furthermore, we show how, using these operators, it is possible to reconcile small corrections to effective field theory correlators with the unitarity of black hole evaporation. We address and resolve all other arguments, advanced in A. Almheiri et al. J. High Energy Phys. 09 (2013) 018 and D. Marolf and J. Polchinski, Phys. Rev. Lett. 111, 171301 (2013), in favor of structure at the black hole horizon. We extend our construction to states that are near equilibrium, and thereby also address the ``frozen vacuum'' objections of R. Bousso, Phys. Rev. Lett. 112, 041102 (2014). Finally, we explore an intriguing link between our construction of interior operators and Tomita-Takesaki theory.

Precision spectroscopy of AdS / CFT

Abstract: We extend recent remarkable progress in the comparison of the dynamical energy spectrum of rotating closed strings in AdS5 ×S 5 and the scaling weights of the corresponding non-near-BPS operators in planar N = 4 supersymmetric gauge theory. On the string side the computations are feasible, using semiclassical methods, if angular momentum quantum numbers are large. This results in a prediction of gauge theory anomalous dimensions to all orders in the ‘t Hooft coupling λ. On the gauge side the direct computation of these dimensions is feasible, using a recently discovered relation to integrable (super) spin chains, provided one considers the lowest order in λ. This oneloop computation then predicts the small-tension limit of the string spectrum for all (i.e. small or large) quantum numbers. In the overlapping window of large quantum numbers and small effective string tension, the string theory and gauge theory results are found to match in a mathematically highly nontrivial fashion. In particular, we compare energies of states with (i) two large angular momenta in S 5 , and (ii) one large angular momentum in AdS5 and S 5 each, and show that the solutions are related by an analytic continuation. Finally, numerical evidence is presented on the gauge side that the agreement persists also at higher (two) loop order.

Spacetime and the holographic renormalization group

Abstract: Anti-de Sitter (AdS) space can be foliated by a family of nested surfaces homeomorphic to the boundary of the space. We propose a holographic correspondence between theories living on each surface in the foliation and quantum gravity in the enclosed volume. The flow of observables between our ``interior'' theories is described by a renormalization group equation. The dependence of these flows on the foliation of space encodes bulk geometry.

Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories.

Abstract: We introduce a new optimization procedure for Euclidean path integrals, which compute wave functionals in conformal field theories (CFTs). We optimize the background metric in the space on which the path integration is performed. Equivalently, this is interpreted as a position-dependent UV cutoff. For two-dimensional CFT vacua, we find the optimized metric is given by that of a hyperbolic space, and we interpret this as a continuous limit of the conjectured relation between tensor networks and Anti--de Sitter (AdS)/conformal field theory (CFT) correspondence. We confirm our procedure for excited states, the thermofield double state, the Sachdev-Ye-Kitaev model, and discuss its extension to higher-dimensional CFTs. We also show that when applied to reduced density matrices, it reproduces entanglement wedges and holographic entanglement entropy. We suggest that our optimization prescription is analogous to the estimation of computational complexity.