PP-Wave / CFT_2 Duality

TL;DR

This paper explores the duality between string theory in a pp-wave background and a symmetric orbifold conformal field theory, revealing detailed correspondences in spectra and state structures, including surprising scaling behaviors.

Contribution

It proposes a detailed duality between fundamental strings in pp-wave backgrounds and the Sym_N(K3) CFT, with novel insights into the scaling of the genus expansion parameter.

Findings

Ground states and genus expansion parameters match in the orbifold limit.

Massive string oscillators correspond to twisted Virasoro generators.

Complete agreement in a special case with one NS 5-brane.

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.