Explicit Formulas for Neumann Coefficients in the Plane-Wave Geometry

Abstract

We obtain explicit formulas for the Neumann coefficients and associated quantities that appear in the three-string vertex for type IIB string theory in a plane-wave background, for any value of the mass parameter mu. The derivation involves constructing the inverse of a certain infinite-dimensional matrix, in terms of which the Neumann coefficients previously had been written only implicitly. We derive asymptotic expansions for large mu and find unexpectedly simple results, which are valid to all orders in 1/mu. Using BMN duality, these give predictions for certain gauge theory quantities to all orders in the modified 't Hooft coupling lambda'. A specific example is presented.

28 pages, 2 figures, v2: reference added, new comments and appendix, typos fixed in eqs. (86) and (89)

References in corpus (10)

• Exact anomalous dimensions of {\cal N}=4 Yang-Mills operators with large R charge
• BMN Correlators and Operator Mixing in N=4 Super Yang-Mills Theory
• Operator Mixing and the BMN Correspondence
• More comments on superstring interactions in the pp-wave background
• Three-point functions in N=4 Yang-Mills theory and pp-waves
• A Calculation of the plane wave string Hamiltonian from N=4 super-Yang-Mills theory
• Tracing the String: BMN correspondence at Finite J^2/N
• Bit Strings from N=4 Gauge Theory
• PP-wave/Yang-Mills Correspondence: An Explicit Check
• Comments on Superstring Interactions in a Plane-Wave Background

Cited by in corpus (49)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Lectures on the Plane-Wave String/Gauge Theory Duality
• Tracing the String: BMN correspondence at Finite J^2/N
• Exact expressions for quantum corrections to spinning strings
• TASI 2003 Lectures on AdS/CFT
• String interactions in gravitational wave backgrounds
• Resolving the Holography in the Plane-Wave Limit of AdS/CFT Correspondence
• String field theory vertex from integrability
• Strings in plane wave backgrounds
• A light-cone approach to three-point functions in AdS_5 x S^5
• On light-cone SFT contact terms in a plane wave
• The Generalized Stieltjes Transform and Its Inverse
• SYM Description of PP-wave String Interactions: Singlet Sector and Arbitrary Impurities
• On the plane-wave cubic vertex
• The superstring Hagedorn temperature in a pp-wave background
• Derivation of String Field Theory from the Large N BMN Limit
• Conformal Dimensions of Two-Derivative BMN Operators
• An alternative formulation of light-cone string field theory on the plane wave
• Correspondence between the 3-point BMN correlators and the 3-string vertex on the pp-wave
• On the exact open-closed vertex in plane-wave light-cone string field theory
• Note on Plane Wave Quantum Mechanics
• Open+Closed String Field Theory From Gauge Fields
• 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
• Holographic cubic vertex in the pp-wave
• Light-Cone String Field Theory in a Plane Wave Background
• BMN operators with three scalar impurites and the vertex--correlator duality in pp-wave
• Impurity Non-Preserving 3-Point Correlators of BMN Operators from PP-Wave Holography I : Bosonic Excitations
• New tests of the pp-wave correspondence
• Divergence Cancellation and Loop Corrections in String Field Theory on a Plane Wave Background
• D-branes in PP-wave light cone string field theory
• AdS/CFT v.s. String Loops
• New aspects of the BMN correspondence beyond the planar limit
• Holography at string field theory level: Conformal three point functions of BMN operators
• DLCQ String Spectrum from $\mathcal{N}=2$ SYM Theory
• Decay widths of three-impurity states in the BMN correspondence
• Three-point functions at strong coupling in the BMN limit
• Decay Modes of Unstable Strings in Plane-Wave String Field Theory
• Three-BMN Correlation Functions: Integrability vs. String Field Theory One-Loop Mismatch
• Strings on Plane Waves, Super-Yang Mills in Four Dimensions, Quantum Groups at Roots of One
• Light-cone Superstring Field Theory, pp-wave background and integrability properties
• The Three-String Vertex for a Plane-Wave Background
• Four-Impurity Operators and String Field Theory Vertex in the BMN Correspondence
• Cubic interactions in the BMN limit of AdS(3) x S(3)
• A note on the uniqueness of the Neumann matrices in the plane-wave background
• Aspects of Supersymmetric Gauge Theory and String Theory
• The AdS/CFT Correspondence: Classical, Quantum, and Thermodynamical Aspects