The Spectrum of Excitations of Holographic Wilson Loops

TL;DR

This paper calculates the spectrum of excitations for holographic Wilson loops in ${ m f N}=4$ SYM, revealing organization into supermultiplets and unifying descriptions across different brane configurations.

Contribution

It explicitly derives the excitation spectrum of D3 branes and discusses the organization of modes into supermultiplets, advancing understanding of holographic Wilson loop excitations.

Findings

D3 brane excitations form supermultiplets of $OSp(4^*|4)$

Fundamental string modes form an ultra-short supermultiplet

Partial spectrum known for D5 brane, likely filling supermultiplets

Abstract

In the holographic framework, a half BPS Wilson loop in ${\cal N}=4$ supersymmetric Yang-Mills in the fundamental, symmetric or antisymmetric representation of SU(N), is best described by a fundamental string, a D3 brane or a D5 brane with fluxes in their worldvolumes, respectively. We derive the spectrum of excitations of such D3 brane in $AdS_5\times S^5$ explicitly, considering its action in both the bosonic and the fermionic sectors, and demonstrate that it is organized according to short multiplets of the supergroup $OSp(4^*|4)$. We also show that the modes of the fundamental string form an ultra-short multiplet of this supergroup. In the case of the D5 brane the bosonic spectrum is only partially known but we argue that it also fills representations of $OSp(4^*|4)$. This way we provide a step towards a unifying picture for the description of holographic excitations of the circular and straight supersymmetric Wilson loops in arbitrary representations.