Construction of the Zero-Energy State of SU(2)-Matrix Theory: Near the Origin

TL;DR

This paper explicitly constructs a unique zero-energy state in SU(2) matrix theory, demonstrating its form at the origin and its relation to supersymmetry and fermionic degrees of freedom in 10D super Yang-Mills.

Contribution

It provides the first explicit construction of the zero-energy state in SU(2) matrix theory, clarifying its structure at the origin and its supersymmetric properties.

Findings

Constructed a unique Spin(9)xSU(2) singlet state.

Showed the state reduces to phi at the origin.

Linked the state to supersymmetry constraints.

Abstract

We explicitly construct a (unique) Spin(9)xSU(2) singlet state, phi, involving only the fermionic degrees of freedom of the supersymmetric matrix-model corresponding to reduced 10-dimensional super Yang-Mills theory, resp. supermembranes in 11-dimensional Minkowski space. Any non-singular wavefunction annihilated by the 16 supercharges of SU(2) matrix theory must, at the origin (where it is assumed to be non-vanishing) reduce to phi.