New tests of the pp-wave correspondence

Abstract

The pp-wave/SYM correspondence is an equivalence relation, H_{string}= Delta -J, between the Hamiltonian H_{string} of string field theory in the pp-wave background and the dilatation operator Delta in N=4 Super Yang-Mills in the double scaling limit. We calculate matrix elements of these operators in string field theory and in gauge theory.In the string theory Hilbert space we use the natural string basis,and in the gauge theory we use the basis which is isomorphic to it. States in this basis are specific linear combinations of the original BMN operators, and were constructed previously for the case of two scalar impurities. We extend this construction to incorporate BMN operators with vector and mixed impurities. This enables us to verify from the gauge theory perspective two key properties of the three-string interaction vertex of Spradlin and Volovich: (1) the vanishing of the three-string amplitude for string states with one vector and one scalar impurity; and (2) the relative minus sign in the string amplitude involving states with two vector impurities compared to that with two scalar impurities. This implies a spontaneous breaking of the Z_2 symmetry of the string field theory in the pp-wave background. Furthermore, we calculate the gauge theory matrix elements of Delta -J for states with an arbitrary number of scalar impurities. In all cases we find perfect agreement with the corresponding string amplitudes derived from the three-string vertex.

40 pages, 9 figures

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Cited by in corpus (15)

• Resolving the Holography in the Plane-Wave Limit of AdS/CFT Correspondence
• Impurity Non-Preserving 3-Point Correlators of BMN Operators from PP-Wave Holography II : Fermionic Excitations
• Fermion BMN operators, the dilatation operator of N=4 SYM, and pp-wave string interactions
• The Duality between IIB String Theory on PP-wave and N=4 SYM: a Status Report
• Holographic cubic vertex in the pp-wave
• Holographic three-point correlators in the Schrodinger/dipole CFT correspondence
• BMN Operators from Wilson Loop
• New aspects of the BMN correspondence beyond the planar limit
• Non-perturbative effects in the BMN limit of N=4 supersymmetric Yang-Mills
• String theory on the Schrodinger pp-wave background
• Mixing of the RR and NSNS sectors in the BMN limit
• Giant Gravitons on the Schrodinger pp-wave geometry
• Four-Impurity Operators and String Field Theory Vertex in the BMN Correspondence
• Local Commutativity and Causality in Interacting PP-wave String Field Theory
• Entanglement Entropy of the N=4 SYM spin chain