Strings in homogeneous gravitational waves and null holography

Abstract

Homogeneous gravitational wave backgrounds arise as infinite momentum limits of many geometries with a well-understood holographic description. General global aspects of these geometries are discussed. Using exact CFT techniques, strings in pp-wave backgrounds supported by a Neveu-Schwarz flux are quantized. As in Euclidean $AdS_3$, spectral flow and associated long strings are shown to be crucial in obtaining a complete spectrum. Holography is investigated using conformally flat coordinates analogous to those of the Poincar\'e patch in AdS. It is argued that the holographic direction is the light-cone coordinate $u$, and that the holographic degrees of freedom live on a codimension-one screen at fixed $u$. The usual conformal symmetry on the boundary is replaced by a representation of a Heisenberg-type algebra $H_D\times H_D$, hinting at a new class of field theories realizing this symmetry. A sample holographic computation of 2 and 3-point functions is provided and Ward identities are derived. A complementary screen at fixed $v$ is argued to be necessary in order to encode the vacuum structure.