Yang-Mills Flux Tube in AdS

TL;DR

This work studies confining flux tubes placed in AdS as conformal defects on the boundary, introducing a dimensionless coupling $\lambda = R_{AdS}\Lambda_{QCD}$ to interpolate between weakly coupled YM in AdS and an effective string description at large radius. A central object is the displacement operator of protected dimension $\Delta=2$, which bridges gauge-field insertions at small $R$ and worldsheet Goldstone modes at large $R$, enabling a principled comparison of two perturbative pictures. The authors perform a detailed weak-coupling computation in planar 3D YM by dimensional reduction to AdS$_2$, deriving KK-mode boundary data, propagators, Feynman rules, and tree-level defect OPE coefficients, and they derive nonlinearly realized conformal constraints to extract leading anomalous dimensions for the first several KK modes. Their results support a smooth, monotonic interpolation across radii without level crossings in a given defect sector, and they sketch how this program could illuminate confinement physics and possibly extend to 4D YM with an axion on the worldsheet. Overall, the paper proposes a concrete, testable route to connect gauge-field degrees of freedom with emergent string-like dynamics via AdS occupancy and defect CFT data.

Abstract

We initiate the study of flux tubes in confining gauge theories placed in a rigid AdS background, which serves as an infrared regulator. Varying the AdS radius from large to small allows us to interpolate between the flat space confining string, and a weakly coupled string-like object which is held together by the AdS gravitational potential. At any radius, the string preserves a subgroup of AdS isometries equivalent to the one-dimensional conformal group and hence, from the boundary point of view, can be thought of as a conformal defect. The defect hosts a protected operator, called displacement, which nonlinearly realizes the broken AdS isometries. At small radius the displacement corresponds to the gauge field strength inserted at the boundary, while at large radius it is mapped to the Goldstone mode living on the string worldsheet. This relates gauge field and worldsheet degrees of freedom. We propose a hypothesis according to which the large and small radius perturbative expansions can be smoothly matched with each other. As a test, we calculate the leading order corrections to the scaling dimensions and OPE coefficients of a set of defect operators at weak coupling in planar 3D Yang-Mills.

Figures (5)

• Figure 1: Flux tube in AdS generated by a pair of Wilson lines on the boundary. Left: constant-time slice. Right: global EAdS.
• Figure 2: Foliations of AdS$_3$ in a $\tau=\text{const}$ slice. (a) AdS$_2$ slicing with $z=\text{const}$ arcs (red) connecting antipodal points. (b) Poincaré slicing with arcs (blue) perpendicular to the boundary.
• Figure 3: Rough expectation for the behavior of OPE coefficients (left) and dimensions (right) as a function of $\lambda = R \Lambda_\text{QCD}$. The absence of level crossing leads to a prediction for which operator is continuously connected to which operator, for the first few low lying operators. By studying the magnitude of the leading perturbative corrections, we can extend the predictions to higher operators. ++ operators are in blue, -+ in green and -- in red.
• Figure 4: The starting point of the analysis leading to the homogeneous identities. The term in the RHS of the first row is evaluated as the integral of the displacement operators. The second row consists of the sum of actions on each of the local operators.
• Figure 5: The identity that leads to the inhomogeneous constraint \ref{['inhomo']}. The blue line corresponds to an unbroken generator, while the red lines correspond to the broken generators. The main step is the second equality, where we replace an unbroken generator by a commutator of $2$ broken generators.