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

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

2002-06-07

arxiv.org/abs/hep-th/0206062v1

JHEP 0207 (2002) 016

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, LaTeX

Scientific paper

10.1088/1126-6708/2002/07/016

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.

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