Proving the PP-Wave/CFT_2 Duality

Abstract

We study the duality between IIB string theory on a pp-wave background, arising as a Penrose limit of the AdS_3 times S^3 times M, where M is T^4 (or K3), and the 2D CFT which is given by the N=(4,4) orbifold (M)^N/S_N, resolved by a blowing-up mode. After analizying the action of the supercharges on both sides, we establish a correspondence between the states of the two theories. In particular and for the T^4 case, we identify both massive and massless oscillators on the pp-wave, with certain classes of excited states in the resolved CFT carrying large R-charge n. For the former, the excited states involve fractional modes of the generators of the N=4 chiral algebra acting on the Z_n ground states. For the latter, they involve, fractional modes of the U(1)^4_L times U(1)^4_R super-current algebra acting on the Z_n ground states. By using conformal perturbation theory we compute the leading order correction to the conformal dimensions of the first class of states, due to the presence of the blowing up mode. We find agreement, to this order, with the corresponding spectrum of massive oscillators on the pp-wave. We also discuss the issue of higher order corrections.

33 pages

References in corpus (4)

• Exact anomalous dimensions of {\cal N}=4 Yang-Mills operators with large R charge
• PP-Wave / CFT_2 Duality
• Rotating deformations of AdS_3\times S^3, the orbifold CFT and strings in the pp-wave limit
• Superstrings on PP-Wave Backgrounds and Symmetric Orbifolds

Cited by in corpus (67)

• Integrability and the AdS(3)/CFT(2) correspondence
• Diagrams for Symmetric Product Orbifolds
• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• Integrability, spin-chains and the AdS3/CFT2 correspondence
• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Giant magnons in the D1-D5 system
• A Spin Chain for the Symmetric Product CFT_2
• Deforming the D1D5 CFT away from the orbifold point
• Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
• S-matrix for magnons in the D1-D5 system
• Excitations in the deformed D1D5 CFT
• Effect of the deformation operator in the D1D5 CFT
• Operator mixing for string states in the D1-D5 CFT near the orbifold point
• Lifting of D1-D5-P states
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Effect of the twist operator in the D1D5 CFT
• $Ad{S}_3/CF{T}_2$, finite-gap equations and massless modes
• Bogoliubov coefficients for the twist operator in the D1D5 CFT
• Boundary entropy of supersymmetric Janus solutions
• Evolution of entanglement entropy in the D1-D5 brane system
• Twist-nontwist correlators in M^N/S_N orbifold CFTs
• Comments on the $S_N$ orbifold CFT in the large $N$-limit
• Lifting at higher levels in the D1D5 CFT
• Analyzing the squeezed state generated by a twist deformation
• Lifting 1/4-BPS States in $Ad{S}_3\times S^3\times T^4$
• Counting Superstrata
• Operator mixing in deformed D1D5 CFT and the OPE on the cover
• Beyond the Tensionless Limit: Integrability in the Symmetric Orbifold
• Full action of two deformation operators in the D1D5 CFT
• D-branes in PP-Waves and Massive Theories on Worldsheet with Boundary
• Lifting of level-1 states in the D1D5 CFT
• BPS Chaos
• Notes on Giant Gravitons on PP-waves
• Conformal Perturbation Theory for Twisted Fields
• Universal lifting in the D1-D5 CFT
• String amplitudes in the Hpp-wave limit of AdS3xS3
• Lifting of states in 2-dimensional $N=4$ supersymmetric CFTs
• One-Loop Transition Amplitudes in the D1D5 CFT
• Thermal Partition Function of Superstring on Compactified PP-Wave
• Intertwining Relations for the Deformed D1D5 CFT
• Multi-centered D1-D5 solutions at finite B-moduli
• The large $N$ limit of OPEs in symmetric orbifold CFTs with $\mathcal{N}=(4,4)$ supersymmetry
• The Tensionless Limit of Pure-Ramond-Ramond AdS3/CFT2
• Component twist method for higher twists in D1D5 CFT
• Thermalization in the D1D5 CFT
• A toy black hole S-matrix in the D1-D5 CFT
• Bosonization, cocycles, and the D1-D5 CFT on the covering surface
• Superstrings on NSNS PP-Waves and Their CFT Duals
• Dynamical evolution in the D1D5 CFT
• Bootstrapping the effect of the twist operator in symmetric orbifold CFTs
• String Theory on Dp-plane waves
• The Dual of a Tidal Force in the D1D5 CFT
• On the massless modes of the AdS3/CFT2 integrable systems
• D-branes in the NS5 Near-horizon pp-Wave Background
• Perturbed symmetric-product orbifold: first-order mixing and puzzles for integrability
• Brane Solutions with/without Rotation in PP-wave Spacetime
• Boundary states in the Nappi-Witten model
• Fortuity and Supergravity
• Strings on Plane Waves and AdS x S
• Second order effect of twist deformation in the D1D5 CFT
• Interpolating between multi-center microstate geometries
• Pulsating strings from two dimensional CFT on $(T^4{)}^N/S(N)$
• Type IIB String Backgrounds on Parallelizable PP-Waves and Conformal Liouville Theory
• A New Supersymmetry Index for the D1-D5 CFT
• Penrose limit for holographic duals of $J\bar{T}$ deformations
• The Resolved Elliptic Genus and the D1-D5 CFT