Towards multi-scale dynamics on the baryonic branch of Klebanov-Strassler

TL;DR

This work advances holographic modeling of genuinely multi-scale dynamical field theories by explicitly constructing a new class of type-IIB backgrounds that generalize the baryonic branch of Klebanov-Strassler using a rotation as a solution-generating technique in the Papadopoulos-Tseytlin framework. It provides a field-theory interpretation in which a dim-2 VEV (baryonic branch) and dim-6 VEV emerge, while a dim-8 operator in the UV can be switched off by fine-tuning a parameter to yield a UV-complete quiver theory reminiscent of KS; below the scale ρ*, Higgsing reduces the effective gauge group and degrees of freedom. The paper analyzes UV and IR behavior, including central charge and Maxwell charge reductions, and demonstrates confinement and a first-order phase transition in the quark-antiquark potential that depends on ρ*, thereby illuminating how multi-scale dynamics arise in a controlled gravity dual. These results offer a concrete holographic platform for exploring walking-like behavior, potential dilaton states, and the role of mild IR singularities, with implications for strongly coupled beyond-Standard-Model dynamics and technicolor-like scenarios.

Abstract

We construct explicitly a new class of backgrounds in type-IIB supergravity which generalize the baryonic branch of Klebanov-Strassler. We apply a solution-generating technique that, starting from a large class of solutions of the wrapped-D5 system, yields the new solutions, and then proceed to study in detail their properties, both in the IR and in the UV. We propose a simple intuitive field theory interpretation of the rotation procedure and of the meaning of our new solutions within the Papadopoulos-Tseytlin ansatz, in particular in relation to the duality cascade in the Klebanov-Strassler solution. The presence in the field theory of different VEVs for operators of dimensions 2, 3 and 6 suggests that this is an important step towards the construction of the string dual of a genuinely multi-scale (strongly coupled) dynamical model.

Figures (7)

• Figure 1: Examples of the background functions $P$, $e^{2\Phi}$ and $\frac{g_4^2N_c}{8\pi^2}$, obtained by solving the master equation for $N_c=4$. Some integration constants are tuned so that the dilaton is kept constant in the IR and UV. The backgrounds differ by the different value of the scale $\rho_{\ast}$.
• Figure 2: Three exact BPS backgrounds in the PT system, obtained numerically. In blue (continuum line) a numerical solution for the wrapped-D5 system, obtained by solving the master equation. In red (long-dashed line) the result of rotating the solution in blue, and fine-tuning $k_2$. In green (short-dashing) a regular KS solution, obtained by matching (where possible) the boundary conditions.
• Figure 3: The (rotation-invariant) combinations $a^2+e^{2\tilde{g}}-1$ and $x+3p$, as a function of the radial direction $\rho$, for the same backgrounds as in Fig. \ref{['Fig:plotcompare']}, with the same color-coding.
• Figure 4: The left panel shows the central charge as a function of the radial coordinate $\rho$ for a few of the rotated solutions. The right panel shows the same, but for deformations of Klebanov-Strassler given by different values of $f_0$ (the black line corresponds to $f_0 = 0$, i.e. the original solution of Klebanov-Strassler).
• Figure 5: The right panel shows the Maxwell charge $Q_{Maxwell, D3}$ for Klebanov-Strassler (black line), and a few different rotated solutions, the $P$ of which is shown in the left panel.