Note on Plane Wave Quantum Mechanics

Abstract

We study the quantum mechanics of BMN operators with two scalar impurities and arbitrarily many traces, at one loop and all genus. We prove an operator identity which partially elucidates the structure of this quantum mechanics, provides some support for a conjectured formula for the free all genus two-point functions, and demonstrates that a single O(g_2^2) contact term arises in the Hamiltonian as a result of transforming from the natural gauge theory basis to the string basis. We propose to identify the S-matrix of this quantum mechanics with the S-matrix of string theory in the plane-wave background.

(22 pages, harvmac) v2: minor changes

References in corpus (10)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Operator Mixing and the BMN Correspondence
• BMN Gauge Theory as a Quantum Mechanical System
• PP-Wave Light-Cone Superstring Field Theory
• Explicit Formulas for Neumann Coefficients in the Plane-Wave Geometry
• On light-cone SFT contact terms in a plane wave
• SYM Description of PP-wave String Interactions: Singlet Sector and Arbitrary Impurities
• BMN operators and string field theory
• Strong Evidence In Favor OF The Existence Of S-Matrix For Strings In Plane Waves

Cited by in corpus (19)

• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Stringing Spins and Spinning Strings
• Tiny Graviton Matrix Theory: DLCQ of IIB Plane-Wave String Theory, A Conjecture
• Lectures on the Plane-Wave String/Gauge Theory Duality
• Strings in plane wave backgrounds
• Spin bit models from non-planar N=4 SYM
• An alternative formulation of light-cone string field theory on the plane wave
• Open+Closed String Field Theory From Gauge Fields
• 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
• Light-Cone String Field Theory in a Plane Wave Background
• Testing Holographic Principle from Logarithmic and Higher Order Corrections to Black Hole Entropy
• New tests of the pp-wave correspondence
• Instability and Degeneracy in the BMN Correspondence
• Type II pp-wave Matrix Models from Point-like Gravitons
• New aspects of the BMN correspondence beyond the planar limit
• Decay widths of three-impurity states in the BMN correspondence
• Four-Impurity Operators and String Field Theory Vertex in the BMN Correspondence