Open AccessRealizations of Conformal and Heisenberg Algebras in PP-wave-CFT Correspondence
Author(s) -
Sumit R. Das,
César Gómez
Publication year - 2002
Publication title -
journal of high energy physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.998
H-Index - 261
eISSN - 1126-6708
pISSN - 1029-8479
DOI - 10.1088/1126-6708/2002/07/016
Subject(s) - physics , conformal field theory , homogeneous space , central charge , limit (mathematics) , conformal map , mathematical physics , theoretical physics , realization (probability) , charge (physics) , contraction (grammar) , field (mathematics) , quantum electrodynamics , quantum mechanics , pure mathematics , mathematics , geometry , philosophy , mathematical analysis , linguistics , statistics
We elaborate on the symmetry breaking pattern involved in the Penrose limitof $AdS_{d+1} \times S^{d+1}$ spacetimes and the corresponding limit of the CFTdual. For d=2 we examine in detail how the symmetries contract to products ofrotation and Heisenberg algebras, both from the bulk and CFT points of view.Using a free field realization of these algebras acting on products ofelementary fields of the CFT with SO(2) R charge +1, we show that this processof contraction restricts all the fields to a few low angular momentum modes andensures that the field with R charge -1 does not appear. This provides anunderstanding of several important aspects of the proposal of Berenstein,Maldacena and Nastase. We also indicate how the contraction can be performed oncorrelation functions.Comment: 24 pages, LaTe
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