Stress Tensor of Static Dipoles in strongly coupled $\cal{N}$=4 Gauge Theory

TL;DR

This work uses the AdS/CFT correspondence to compute the holographic stress tensor of static electric and electric-magnetic dipoles in strongly coupled $\mathcal{N}=4$ SYM by solving the linearized Einstein equations with Maldacena-string sources in $AdS_5$. It derives general methods to extract the boundary stress tensor from bulk metric perturbations, and applies them to single-quark, dipole, and dyon-like configurations, obtaining far-field scalings of $~1/|y|^7$ and near-field behavior dominated by the charge(s) themselves. The results show significant quantitative differences from weak coupling, including angular distributions and magnitudes, and reveal that the boundary stress pattern resembles polarization clouds rather than a visible string, with implications for interpreting flux-tube-like structures in QCD-like theories at strong coupling. The study also points to potential connections with quasi-conformal QCD-like plasmas and suggests future work on dynamical, non-equilibrium configurations and their hydrodynamic limits. All findings are consistent with conformal invariance and provide a framework for exploring stress-tensor imprints of bulk sources in strongly coupled gauge theories.

Abstract

In the context of the AdS/CFT correspondence we calculate the induced stress tensor of static dipoles (electric-electric and electric-magnetic) in a strongly coupled ${\cal N}=4$ SYM gauge theory, by solving the linearized Einstein equation with Maldecena string as a source. Analytic expressions are given for the far-field and a near-field close to one charge, and compared to what one has in weak coupling. The result can be compared to lattice results for QCD-like theories in a deconfined but strongly coupled regime.

Figures (3)

• Figure 1: (Color online) The far field energy distribution in polar angle $\theta (cos(\theta)=y_1/\lvert y\rvert)$, normalized at zero angle. Solid (black) line is our result, compared to the perturbative result $(3cos^2+1)/4$ given by the dashed (blue) line.
• Figure 2: (color online) Schematic demonstration of the pending string and the propagators of stress tensor. The source is at the point $A$ integrated over string, it either (a) goes directly to the observation point $y$ via bulk-to-boundary propagates(dashed line) , or (b) first transforms to $s^h_{mn}$ in some other point $B$ via bulk-to-bulk propagator(dash-dotted line), then goes to the observation point
• Figure 3: (color online) The integrands of the $z$ integral along the string for $Q_{00}^1$(blue dotted),$Q_{00}^2$ (green dashed) and their sum(red solid), with $z_m=1$