Realizations of Conformal and Heisenberg Algebras in PP-wave-CFT Correspondence

TL;DR

This paper explores how symmetries in AdS/CFT correspondence contract to simpler algebraic structures in the Penrose limit, revealing insights into the duality and field behavior in the pp-wave background.

Contribution

It provides a detailed analysis of symmetry contraction from AdS to pp-wave backgrounds and demonstrates how this affects field modes and correlation functions in the dual CFT.

Findings

Symmetry contracts to rotation and Heisenberg algebras in the Penrose limit.

Field modes are restricted to low angular momentum states.

The contraction process influences correlation functions in the CFT.

Abstract

We elaborate on the symmetry breaking pattern involved in the Penrose limit of $AdS_{d+1} \times S^{d+1}$ spacetimes and the corresponding limit of the CFT dual. For d=2 we examine in detail how the symmetries contract to products of rotation and Heisenberg algebras, both from the bulk and CFT points of view. Using a free field realization of these algebras acting on products of elementary fields of the CFT with SO(2) R charge +1, we show that this process of contraction restricts all the fields to a few low angular momentum modes and ensures that the field with R charge -1 does not appear. This provides an understanding of several important aspects of the proposal of Berenstein, Maldacena and Nastase. We also indicate how the contraction can be performed on correlation functions.