Note on Plane Wave Quantum Mechanics

TL;DR

This paper investigates the quantum mechanics of BMN operators with multiple traces at one loop and all genus, revealing an operator identity, a contact term in the Hamiltonian, and proposing an S-matrix correspondence with string theory.

Contribution

It introduces a key operator identity, supports a conjectured formula for two-point functions, and links the quantum mechanics S-matrix to string theory in the plane-wave background.

Findings

Proves an operator identity for BMN operators.

Identifies a contact term in the Hamiltonian at order g_2^2.

Proposes the S-matrix correspondence with string theory.

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.