Disordered Systems and the Replica Method in AdS/CFT

Abstract

We formulate a holographic description of effects of disorder in conformal field theories based on the replica method and the AdS/CFT correspondence. Starting with $n$ copies of conformal field theories, randomness with a gaussian distribution is described by a deformation of double trace operators. After computing physical quantities, we take the $n\to 0$ limit at the final step. We compute correlation functions in the disordered systems by using the holographic replica method as well as the formulation in the conformal field theory. We find examples where disorder changes drastically the scaling of two point functions. The renormalization group flow of the effective central charge in our disordered systems is also discussed.

26 pages, references added, published version

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• Webs in multiparton scattering using the replica trick
• Transport Properties of Holographic Defects
• Decoupling with random quantum circuits
• Free Energy from Replica Wormholes
• Fast scrambling on sparse graphs
• Holographic applications of logarithmic conformal field theories
• General properties of multiparton webs: proofs from combinatorics
• Interacting String Multi-verses and Holographic Instabilities of Massive Gravity
• On holographic disorder-driven metal-insulator transitions
• Adventures in Holographic Dimer Models
• A Dirty Holographic Superconductor
• Quantitative approaches to information recovery from black holes
• Disordered Holographic Systems I: Functional Renormalization
• Holographic Conductivity in Disordered Systems
• Behind the geon horizon
• Josephson Junctions and AdS/CFT Networks
• Holographic p-wave Superconductor with Disorder
• Disorder in Large-N Theories
• A smeared quantum phase transition in disordered holography
• Perturbatively charged holographic disorder
• A family of super Schrodinger invariant Chern-Simons matter systems
• Towards a Holographic Bose-Hubbard Model
• Mimic the optical conductivity in disordered solids via gauge/gravity duality
• From Maxwell-Chern-Simons theory in $Ad{S}_3$ towards hydrodynamics in 1+1 dimensions
• Gravity duals for logarithmic conformal field theories
• One-Shot Randomized and Nonrandomized Partial Decoupling
• Traversable AdS Wormhole via Non-local Double Trace or Janus Deformation
• Possible Anderson localization in a holographic superconductor
• Thermodynamics of Holographic Defects
• Probing AdS Wormholes by Entanglement Entropy
• Coherence effects in disordered geometries with a field-theory dual
• Marginal and Irrelevant Disorder in Einstein-Maxwell backgrounds
• On 1-loop diagrams in AdS space and the random disorder problem
• Correlation functions in the holographic replica method
• Photoemission "experiments" on holographic lattices
• Finite Size Scaling in Quantum Hallography
• Spatially Random Disorder in Unitary Fermion System in $(4-\epsilon )$-Dimensions and Effective Action at Finite Temperature
• Disorder in AdS${}_3$/CFT${}_2$
• Seeing bulk perturbations in Lifshitz holography
• Quench Disorder and Scalar Field Theory in the Presence of Boundary