Two-Loop Partition Function in the Planar Plane-Wave Matrix Model

TL;DR

This paper calculates the two-loop partition function of the plane-wave matrix model using two independent methods, confirming their agreement and exploring the model's symmetry and integrability properties.

Contribution

It provides the first independent verification of the two-loop partition function in the plane-wave matrix model through two different computational approaches.

Findings

Results from both calculations agree precisely.

Polynomials in the result have special properties linked to symmetry or integrability.

Supports the conjectured duality with little string theory.

Abstract

We perform two independent calculations of the two-loop partition function for the large N 't Hooft limit of the plane-wave matrix model, conjectured to be dual to the decoupled little string theory of a single spherical type IIA NS5-brane. The first is via a direct two-loop path-integral calculation in the matrix model, while the second employs the one-loop dilatation operator of four-dimensional N = 4 Yang-Mills theory truncated to the SU(2|4) subsector. We find precise agreement between the results of the two calculations. Various polynomials appearing in the result have rather special properties, possibly related to the large symmetry algebra of the theory or to integrability.