Wilson Loops in string duals of Walking and Flavored Systems

TL;DR

This work uses gauge-string duality to probe non-local operators in field theories with walking dynamics and fundamental flavors by analyzing Wilson loops via classical string probes in Type IIB backgrounds generated by D5 branes. It develops a general formalism for the Qar{Q} potential and separation from the Nambu-Goto action, and applies it to well-known AdS/CFT examples to calibrate the method. It then constructs and analyzes walking D5 backgrounds (unflavored) and flavored variants, uncovering distinct IR walking regions, two characteristic scales, and a complex multi-branch structure for the Wilson-loop energy as a function of separation, including cusp formation and stability considerations. The results show that walking dynamics imprint observable changes in the Wilson loop phenomenology, such as a larger linear potential slope and a finite maximum separation in flavored cases, offering a robust holographic diagnostic for walking and flavor effects with potential relevance to models of dynamical electroweak symmetry breaking.

Abstract

We consider the VEV of Wilson loop operators by studying the behavior of string probes in solutions of Type IIB string theory generated by Nc D5 branes wrapped on an internal manifold. In particular, we focus on solutions to the background equations that are dual to field theories with a walking gauge coupling as well as for flavored systems. We present in detail our walking solution and emphasize various general aspects of the procedure to study Wilson loops using string duals. We discuss the special features that the strings show when probing the region associated with the walking of the field theory coupling.

Figures (10)

• Figure 1: Setting of the string.
• Figure 2: The numerical solutions for $P(\rho)/N_c$ used in the analysis as an example, for $N_c=100$. The three solutions correspond to the $\hat{P}$ case with $\rho_{\ast}=0$, and to two new numerical solutions with, respectively, $\rho_{\ast}\simeq 4$ and $\rho_{\ast}\simeq 9$. The numerical solutions can be plotted up to $\rho\simeq 150$, but in the following we will truncate them at $\rho_{1}=30$.
• Figure 3: The functions $(e^{2g},e^{2h},e^{2k},\phi)$ appearing in the metric for the same solutions as in Fig. \ref{['Fig:numericalP']}, computed rescaling $P\rightarrow P/N_c$, and $Q\rightarrow Q/N_c$.
• Figure 4: The (10-dimensional) Ricci scalar $R$ and the scalar $R^2\equiv R_{MN}R_{PQ}g^{MP}g^{NQ}$, plotted as a function of the radial coordinate $\rho$, for several numerical solutions in the class discussed in the body of the paper. Each curve corresponds to a different value of $\rho_{\ast}$. Notice that both scalars are finite in the $\rho\rightarrow 0$ limit.
• Figure 5: Upper panel, the radial coordinate $\rho_0$ of the middle point of the string as a function of $L_{QQ}$. Middle and lower panel, the energy $E_{QQ}$ as a function of the quark-antiquark separation $E_{QQ}(L_{QQ})$. The three solutions in Fig. \ref{['Fig:numericalP']} are used, with the same color-coding.