Penrose limit, Spontaneous Symmetry Breaking and Holography in PP-Wave Background

TL;DR

This paper explores the holographic duality in pp-wave backgrounds, showing how gauge theories relate to string dynamics and spontaneous symmetry breaking, with implications for understanding Goldstone modes.

Contribution

It demonstrates the holographic relation between string evolution and RG flow in gauge theories, revealing spontaneous symmetry breaking and Goldstone modes in pp-wave backgrounds.

Findings

Gauge theory lives on a Euclidean subspace of transverse coordinates.

String light-cone time evolution corresponds to RG flow.

Spontaneous SO(4,2)×SO(6) symmetry breaking to SO(4)×SO(4).

Abstract

We argue that the gauge theory dual to the Type IIB string theory in ten-dimensional pp-wave background can be thought to `live' on an {\it Euclidean} subspace spanning four of the eight transverse coordinates. We then show that light-cone time evolution of the string is identifiable as the RG flow of the gauge theory -- a relation facilitating `holography' of the pp-wave background. The `holography' reorganizes the dual gauge theory into theories defined over Hilbert subspaces of fixed R-charge. The reorganization breaks the SO(4,2)$\times$SO(6) symmetry to a maximal subgroup SO(4)$\times$ SO(4) spontaneously. We argue that the low-energy string modes may be regarded as Goldstone modes resulting from such symmetry breaking pattern.