Proving the PP-Wave/CFT_2 Duality

TL;DR

This work tests the pp-wave/ CFT_2 duality for IIB string theory on a pp-wave limit of AdS_3×S^3×M (M= T^4 or K3) and the N=(4,4) symmetric-product CFT M^N/S_N blown up by a Z_2 mode. It establishes a detailed state correspondence: ground states ↔ chiral primaries, massive and massless pp-wave oscillators ↔ specific fractional-descendant states in Z_n twisted sectors, with J ~ √N governing the twist. Using conformal perturbation theory around the blowing-up deformation, the authors compute leading corrections to conformal dimensions—finding agreement with the pp-wave spectrum for massive oscillators and revealing distinct scaling for massless modes via fractional U(1)^4 currents—while arguing for an all-order extension of the symmetry algebra that reconciles off-orbifold behavior. The results provide concrete quantitative tests of the duality beyond protected operators and illuminate how moduli movements (blowing up) reorganize short multiplets into long ones. The analysis also highlights open questions about higher-order corrections and the precise all-orders structure connecting the two sides.

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.