The Spectrum of Excitations of Holographic Wilson Loops

TL;DR

This work analyzes quantum excitations of holographic half-BPS Wilson loops in $\mathcal{N}=4$ SYM by examining fluctuations of the D3-brane dual to the symmetric representation, the fundamental string, and the D5-brane dual to the antisymmetric representation in $AdS_5\times S^5$. The bosonic and fermionic open-string fluctuations on the D3-brane are computed and shown to organize into short multiplets of the supergroup $OSp(4^*|4)$, with the fundamental-string modes forming an ultra-short multiplet as well. For the D3-brane, fermions are massless due to a supersymmetric cancellation, and the spectrum is encoded in a KK tower of $AdS_2$ modes with quantum numbers under $SL(2,\mathds{R})\times SO(3)\times SO(5)$. The paper also sketches the (partially known) D5-brane spectrum and argues that, across representations, all holographic excitations fit into the same $OSp(4^*|4)$ framework, paving the way toward a unified dynamical description of Wilson-loop probes in holography.

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.