Walking Dynamics from String Duals

TL;DR

The paper addresses realizing walking technicolor within a calculable holographic framework. It constructs a Type IIB background from wrapped D5-branes and analyzes a master equation for the function $P( ho)$ to obtain a four-dimensional gauge coupling $oldsymbol{ extlambda} = g^2 N_c/(8\pi^2)$ that shows a walking plateau, enabling controlled RG flow from UV to IR. The work identifies three distinct dynamical scales, $oldsymbol{ extLambda_*}$ (walking), $oldsymbol{ extLambda}$ (symmetry breaking), and $oldsymbol{ extLambda_0}$ (confinement), and provides an operator-based interpretation with a dimension-6 deformation, a dimension-4 VEV, and a dimension-3 gaugino condensate; it also discusses approximate symmetries and a good IR singularity. This holographic realization offers a calculable platform for exploring walking dynamics, their spectra, and potential couplings to a Standard-Model sector, with implications for electroweak symmetry breaking and beyond-Standard-Model phenomenology.

Abstract

Within the context of a String Theory dual to N=1 gauge theories with gauge group SU(Nc) and large Nc, we identify a class of solutions of the background equations for which a suitably defined dual of the gauge coupling exhibits the features of a walking theory. We find evidence for three distinct, dynamically generated scales, characterizing walking, symmetry breaking and confinement, and we put them in correspondence with field theory by an analysis of the operators driving the flow.

Figures (4)

• Figure 1: Plot of the dilaton $\phi$ as a function of $\rho$. The first three orders in the expansion (\ref{['solution']}) are compared with the numerical solution.
• Figure 2: The background functions $h$, $g$, $k$ and $a$ as a function of $\rho$. Here we plot the first three orders in the expansion (\ref{['solution']}) and we compare it with the numerical solution. It is clear that the expansion (\ref{['solution']}) converges sufficiently fast.
• Figure 3: The 't Hooft coupling $g^2N_c/(8\pi^2)$ as a function of $\rho$ for various values of the parameters $c$, $\alpha$. All three curves are for $N_c=10$, while $c=60$, $\alpha=0.01$ for (i), $c=90$, $\alpha=0.002$ for (ii) and $c=100$, $\alpha=0.0005$ for (iii). The red (long dashes) curves are the ${\cal O}(c)$ approximation in the expansion (\ref{['solution']}), the blue (medium dashes) lines are the ${\cal O}(1/c)$ approximation, the green (short dashes) lines are the ${\cal O}(1/c^3)$ approximation, and the black (dotted) lines are the numerical solutions.
• Figure 4: The three qualitatively different energy regimes and the corresponding operators that dominate the solution in each of these regions.