Conformal fields in the pp-wave limit

Abstract

The pp-wave (Penrose limit) in conformal field theory can be viewed as a special contraction of the unitary representations of the conformal group. We study the kinematics of conformal fields in this limit in a geometric approach where the effect of the contraction can be visualized as an expansion of space-time. We discuss the two common models of space-time as carrier spaces for conformal fields: One is the usual Minkowski space and the other is the coset of the conformal group over its maximal compact subgroup. We show that only the latter manifold and the corresponding conformal representation theory admit a non-singular contraction limit. We also address the issue of correlation functions of conformal fields in the pp-wave limit. We show that they have a well-defined contraction limit if their space-time dependence merges with the dependence on the coordinates of the R symmetry group. This is a manifestation of the fact that in the limit the space-time and R symmetries become indistinguishable. Our results might find applications in actual calculations of correlation functions of composite operators in N=4 super Yang-Mills theory.

LaTex, 32 pages, 1 figure, discussion of correlation functions extended; some corrections made; references added

References in corpus (13)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
• Penrose limits and maximal supersymmetry
• Exactly solvable model of superstring in Ramond-Ramond plane wave background
• A new maximally supersymmetric background of IIB superstring theory
• A New Double-Scaling Limit of N=4 Super Yang-Mills Theory and PP-Wave Strings
• PP-wave string interactions from perturbative Yang-Mills theory
• Operators with large R charge in N=4 Yang-Mills theory
• On lightcone string field theory from Super Yang-Mills and holography
• From Super-AdS_5xS^5 Algebra to Super-pp-wave Algebra
• Penrose limit, Spontaneous Symmetry Breaking and Holography in PP-Wave Background
• PP-Waves and Holography
• Super-PP-wave Algebra from Super-AdS x S Algebras in Eleven-dimensions

Cited by in corpus (19)

• The S-matrix of String Bound States
• PP-Wave Light-Cone Superstring Field Theory
• BMN Operators and Superconformal Symmetry
• String interactions in gravitational wave backgrounds
• Structure of large spin expansion of anomalous dimensions at strong coupling
• Strings in plane wave backgrounds
• Modular Invariance of Strings on PP-Waves with RR-flux
• Penrose Limits, Deformed pp-Waves and the String Duals of N=1 Large n Gauge Theory
• Conformal Dimensions of Two-Derivative BMN Operators
• Correspondence between the 3-point BMN correlators and the 3-string vertex on the pp-wave
• BMN operators with three scalar impurites and the vertex--correlator duality in pp-wave
• N=8 Mechanics in SU(2)xSU(2) Harmonic Superspace
• String amplitudes in the Hpp-wave limit of AdS3xS3
• 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
• PP-wave string interactions from n-point correlators of BMN operators
• N=4 SYM on R times S^3 and PP-Wave
• Cubic interactions in the BMN limit of AdS(3) x S(3)
• N=4 superconformal mechanics in the pp-wave limit