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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.


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TL;DR: In this article, the authors investigated the dimensions of unitary higher-dimensional conformal field theories (CFTs) via the crossing equations in the light-cone limit and found that CFTs become free at large spin and 1/s is a weak coupling parameter.
Abstract: We consider several aspects of unitary higher-dimensional conformal field theories (CFTs). We first study massive deformations that trigger a flow to a gapped phase. Deep inelastic scattering in the gapped phase leads to a convexity property of dimensions of spinning operators of the original CFT. We further investigate the dimensions of spinning operators via the crossing equations in the light-cone limit. We find that, in a sense, CFTs become free at large spin and 1/s is a weak coupling parameter. The spectrum of CFTs enjoys additivity: if two twists τ 1, τ 2 appear in the spectrum, there are operators whose twists are arbitrarily close to τ 1 + τ 2. We characterize how τ 1 + τ 2 is approached at large spin by solving the crossing equations analytically. We find the precise form of the leading correction, including the prefactor. We compare with examples where these observables were computed in perturbation theory, or via gauge-gravity duality, and find complete agreement. The crossing equations show that certain operators have a convex spectrum in twist space. We also observe a connection between convexity and the ratio of dimension to charge. Applications include the 3d Ising model, theories with a gravity dual, SCFTs, and patterns of higher spin symmetry breaking.

607 citations

01 Jan 2009
TL;DR: In this article, it was shown that at the level of linear response the low-frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e., by the "membrane paradigm" fluid of classical black hole mechanics.
Abstract: We show that at the level of linear response the low-frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e., by the ‘‘membrane paradigm’’ fluid of classical black hole mechanics. Thus, generic boundary theory transport coefficients can be expressed in terms of geometric quantities evaluated at the horizon. When applied to the stress tensor this gives a simple, general proof of the universality of the shear viscosity in terms of the universality of gravitational couplings, and when applied to a conserved current it gives a new general formula for the conductivity. Away from the low-frequency limit the behavior of the boundary theory fluid is no longer fully captured by the horizon fluid even within the derivative expansion; instead, we find a nontrivial evolution from the horizon to the boundary. We derive flow equations governing this evolution and apply them to the simple examples of charge and momentum diffusion.

588 citations

Journal ArticleDOI
TL;DR: In this article, a holographic model building approach to ''strange metallic'' phenomenology is proposed, which couples a neutral Lifshitz-invariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, described by D-branes.
Abstract: We initiate a holographic model building approach to `strange metallic' phenomenology. Our model couples a neutral Lifshitz-invariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, dually described by D-branes. In the physical regime of temperature much lower than the charge density and gap, we exhibit anomalous scalings of the temperature and frequency dependent conductivity. Choosing the dynamical critical exponent z appropriately we can match the non-Fermi liquid scalings, such as linear resistivity, observed in strange metal regimes. As part of our investigation we outline three distinct string theory realizations of Lifshitz geometries: from F theory, from polarised branes, and from a gravitating charged Fermi gas. We also identify general features of renormalisation group ow in Lifshitz theories, such as the appearance of relevant charge-charge interactions when z ≥ 2. We outline a program to extend this model building approach to other anomalous observables of interest such as the Hall conductivity.

583 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the set of such constraints for all ball-shaped spatial regions in the CFT is exactly equivalent to the requirement that the dual geometry satisfy the gravitational equations of motion, linearized about pure AdS.
Abstract: Entanglement entropy obeys a ‘first law’, an exact quantum generalization of the ordinary first law of thermodynamics. In any CFT with a semiclassical holographic dual, this first law has an interpretation in the dual gravitational theory as a constraint on the spacetimes dual to CFT states. For small perturbations around the CFT vacuum state, we show that the set of such constraints for all ball-shaped spatial regions in the CFT is exactly equivalent to the requirement that the dual geometry satisfy the gravitational equations of motion, linearized about pure AdS. For theories with entanglement entropy computed by the Ryu-Takayanagi formula S = $ \mathcal{A} $ /(4G N), we obtain the linearized Einstein equations. For theories in which the vacuum entanglement entropy for a ball is computed by more general Wald functionals, we obtain the linearized equations for the associated higher-curvature theories. Using the first law, we also derive the holographic dictionary for the stress tensor, given the holographic formula for entanglement entropy. This method provides a simple alternative to holographic renormalization for computing the stress tensor expectation value in arbitrary higher derivative gravitational theories.

578 citations

Journal ArticleDOI
24 Jul 2009-Science
TL;DR: It is found that the mathematics of string theory is capable of describing fermionic quantum critical states, and the spectral functions of fermions in the field theory are computed.
Abstract: A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.

576 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2021234
2020348
2019387
2018368
2017393
2016413