On the Ground State of the Supersymmetric Five-brane

TL;DR

This paper investigates the existence of a zero-energy supersymmetric ground state for the fundamental five-brane, constructing a perturbative Nicolai map and demonstrating the presence of such a vacuum state.

Contribution

It provides a perturbative construction of the Nicolai map for the five-brane and shows it admits a zero-energy supersymmetric vacuum, a novel result in brane theory.

Findings

The Nicolai map equilibrates at third order in inverse tension.

The five-brane has a normalizable zero-energy supersymmetric vacuum.

Other p-branes, except the three-brane, lack such ground states.

Abstract

We examine if there exists a zero-energy supersymmetric ground state for the fundamental five-brane. Looking for an $SO(6)\times SO(2)$- invariant ground state, we construct, in the light-cone gauge, perturbatively a Nicolai map up to third order in the inverse five-brane tension. We show that the Nicolai map equilibrates and the five-brane has a zero-energy normalizable supersymmetric vacuum state. For the other p-branes, we argue that only the three-brane has a zero-energy ground state.