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

Abstract

We elaborate on the symmetry breaking pattern involved in the Penrose limit of $Ad{S}_{d+1}\times S^{d+1}$ 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.

24 pages, LaTeX

References in corpus (6)

• PP-wave string interactions from perturbative Yang-Mills theory
• Three-point functions in N=4 Yang-Mills theory and pp-waves
• Anomalous dimensions in gauge theories from rotating strings in $Ad{S}_5\times S^5$
• Superstrings on PP-Wave Backgrounds and Symmetric Orbifolds
• More on Penrose Limit of AdS_4 x Q^{1,1,1}
• Penrose limit and string quantization in AdS_3 \times S^3

Cited by in corpus (14)

• Homogeneous Plane Waves
• Selected Topics in the Large Quantum Number Expansion
• Holographic Reformulation of String Theory on AdS_5 x S^5 background in the PP-wave limit
• Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case
• Supersymmetric D3 brane and N=4 SYM actions in plane wave backgrounds
• Spectra of PP-Wave Limits of M-/Superstring Theory on AdS_p x S^q Spaces
• Thermal Partition Function of Superstring on Compactified PP-Wave
• Superstring Vacua of 4-dimensional PP-Waves with Enhanced Supersymmetry
• Penrose limit of AdS(3) X S(3) X S(3) X S(1) and its associated sigma model
• Oscillator Construction of Spectra of PP-Wave Superalgebras in Eleven Dimensions
• N=4 SYM on R times S^3 and PP-Wave
• Strings on Plane Waves, Super-Yang Mills in Four Dimensions, Quantum Groups at Roots of One
• Cubic interactions in the BMN limit of AdS(3) x S(3)
• Propagators and WKB-exactness in the plane wave limit of AdSxS