PP-Wave / CFT_2 Duality

TL;DR

The paper analyzes the Penrose (pp-wave) limit of AdS3×S3×K3 and its dual Sym_N(K3) CFT, proposing that a fundamental string in the pp-wave is dual to the c=6 effective string formed by twist operator-based string bits. It demonstrates leading-order agreement between pp-wave string spectra and CFT states, identifies a finite double-scaling genus expansion with parameter J^2/N, and explicitly matches ground states and many excitations, including a complete match in a special NS5=1 case. The work develops a BMN-like twist-operator framework within the symmetric product CFT, showing how twisted sectors encode string bits and how higher-genus corrections are governed by a J^2/N expansion. It also discusses perturbations away from the orbifold point via marginal Z2 twists, outlining how interactions and higher-order corrections could be captured in this duality.

Abstract

We investigate the pp-wave limit of the AdS_3\times S^3\times K3 compactification of Type IIB string theory from the point of view of the dual Sym_N(K3) CFT. It is proposed that a fundamental string in this pp-wave geometry is dual to the c=6 effective string of the Sym_N(K3) CFT, with the string bits of the latter being composed of twist operators. The massive fundamental string oscillators correspond to certain twisted Virasoro generators in the effective string. It is shown that both the ground states and the genus expansion parameter (at least in the orbifold limit of the CFT) coincide. Surprisingly the latter scales like J^2/N rather than the J^4/N^2 which might have been expected. We demonstrate a leading-order agreement between the pp-wave and CFT particle spectra. For a degenerate special case (one NS 5-brane) an intriguing complete agreement is found.