D-branes in Yang-Mills theory and Emergent Gauge Symmetry

TL;DR

The work argues that a sector of ${ m N}=4$ SU(${N}$) Yang–Mills theory on ${ m S}^3$ contains D-brane-like states (giant gravitons) whose open-string excitations realize a local emergent gauge theory on an auxiliary brane worldvolume. By mapping half-BPS operators to brane configurations via Young diagrams and employing a reduced matrix model, the authors show Gauss’ law emerges from combinatorics, and Chan–Paton factors appear dynamically for strings on multiple branes. They develop a systematic framework to count and construct open-string states using permutation-group methods, yielding results that match Gauss’ law constraints in various two-brane and multi-brane setups, and demonstrate that the emergent gauge group is non-Abelian in the presence of coincident branes. The study further analyzes interaction amplitudes—string splitting and closed-string emission—providing partial dynamical evidence for emergent non-Abelian gauge dynamics and hinting at a deeper holographic, locality-based description of emergent gauge theories from matrix degrees of freedom. Overall, the paper strengthens the bridge between gauge-theory constructions and D-brane/open-string physics in AdS/CFT, highlighting a concrete path to locality and gauge structure arising emergently on brane worldvolumes.

Abstract

Four-dimensional supersymmetric SU(N) Yang-Mills theory on a sphere has highly charged baryon-like states built from anti-symmetric combinations of the adjoint scalars. We show that these states, which are equivalently described as holes in a free fermi sea of a reduced matrix model, are D-branes. Their excitations are stringlike and effectively realize Dirichlet and Neumann boundary conditions in various directions. The low energy brane dynamics should realize an emergent gauge theory that is local on a new space. We show that the Gauss' Law associated to this emergent gauge symmetry appears from combinatorial identities relating the stringy excitations. Although these excitations are not BPS, they can be near-BPS and we can hope to study them in perturbation theory. Accordingly, we show that the Chan-Paton factors expected for strings propagating on multiple branes arise dynamically, allowing the emergent gauge symmetry to be non-Abelian.

Figures (8)

• Figure 1: One string beginning in one giant graviton and ending in another one
• Figure 2: Two strings stretching between two giants with opposite orientations
• Figure 3: The three possible Young tableau of $S_3$ that give different operators under the replacement $1,2 \rightarrow \Phi$ and $3 \rightarrow Y$.
• Figure 4: The decompsition of $S_n$ to $S_{n-1} \times S_1$. The dashed boxes indicate where the single box of $S_1$ can attach (see footnote \ref{['foot']}).
• Figure 5: The decomposion of $S_n\rightarrow S_{n-2} \times S_1 \times S_1$. The dashed boxes indicate where the single boxes of the two $S_1$s can attach. The factor of $2$ indicates that the third $S_{n-2}$ diagram appears twice via the Littlewood-Richardson multiplication rules (see footnote \ref{['foot']}).