Superconformal Quantum Mechanics and the Discrete Light-Cone Quantisation of N=4 SUSY Yang-Mills

TL;DR

This paper explores a superconformal quantum mechanical model derived from N=4 supersymmetric Yang-Mills theory in a specific light-cone quantization, revealing new models with SU(1,1|4) symmetry.

Contribution

It constructs a new family of superconformal quantum mechanical models with explicit generators, emerging in a particular limit of the light-cone quantization of N=4 SYM.

Findings

Superconformal invariance appears as the fiber volume shrinks to zero.

Explicit construction of SU(1,1|4) superconformal generators.

Discovery of a large new class of superconformal quantum mechanical models.

Abstract

We study the quantum mechanical sigma model arising in the discrete light-cone quantisation of N=4 supersymmetric Yang-Mills theory. The target space is a certain torus fibration over a scale-invariant special Kahler manifold. We show that the expected SU(1,1|4) light-cone superconformal invariance of the N=4 theory emerges in a limit where the volume of the fibre goes to zero and give an explicit construction of the generators. The construction given here yields a large new family of superconformal quantum mechanical models with SU(1,1|4) invariance.