Instantons, Integrability and Discrete Light-Cone Quantisation

TL;DR

This paper explores the supersymmetric quantum mechanics on instanton moduli space, revealing integrability, superconformal symmetry, and connections to N=4 SYM's light-cone dilatation operator, with implications for understanding the theory's spectrum.

Contribution

It introduces a model with superalgebraic symmetry that links instanton moduli space to N=4 SYM in DLCQ, highlighting integrability and spectral properties.

Findings

Model exhibits discrete spectrum with wavefunctions supported away from singularities

Hamiltonian is part of superalgebra and becomes superconformal in N=4 sector

Semiclassical analysis reveals integrable scaling limit

Abstract

We study supersymmetric quantum mechanics on the moduli space of Yang-Mills instantons on R^2 x T^2 and its application to the discrete light-cone quantisation (DLCQ) of N=4 SUSY Yang-Mills. In the presence of a target space magnetic field, the model has a discrete spectrum with the wavefunctions of generic energy eigenstates supported away from the singular points of the moduli space. The corresponding Hamiltonian is part of an osp(1,1|4) superalgebra which enlarges to su(1,1|4) superconformal invariance in the sector corresponding to the N=4 theory. The Hamiltonian is isospectral to the light-cone dilatation operator of the N=4 theory in this sector. The model also has an interesting scaling limit where it becomes integrable. We determine the semiclassical spectrum in this limit. We discuss a possible approach to constructing the dilatation operator of N=4 supersymmetric Yang-Mills theory in DLCQ.