Excited States of Open Strings From $\mathcal{N}=4$ SYM

TL;DR

This paper advances the understanding of open string excitations in $ ext{N}=4$ SYM by computing second-order perturbative corrections, revealing a relativistic dispersion relation for the ground state.

Contribution

It introduces a Fock-like space of states using Cuntz oscillators and demonstrates a cancellation among excited states at three-loop order.

Findings

Ground state energy aligns with relativistic dispersion relation

Constructed a Fock-like space for open string states

Performed second-order perturbation theory with three-loop dilatation generator

Abstract

We continue the analysis of building open strings stretched between giant gravitons from $\mathcal{N}=4$ SYM by going to second order in perturbation theory using the three-loop dilatation generator from the field theory. In the process we build a Fock-like space of states using Cuntz oscillators which can be used to access the excited open string states. We find a remarkable cancellation among the excited states that shows the ground state energy is consistent with a fully relativistic dispersion relation.