Bulk Dynamics in Confining Gauge Theories

TL;DR

The work develops a gauge-invariant, sigma-model–covariant framework for bulk fluctuations in a 5D fake-supergravity truncation of type IIB supergravity, enabling controlled analysis of confining gauge theories. Applying the method to MN and KS backgrounds, the authors derive and solve fluctuation equations, obtaining explicit glueball spectra for MN and analytic, UV-focused solutions for KS in the moderate-UV regime, with careful discussion of boundary conditions and singularities. These results demonstrate the feasibility of handling generally coupled scalar bulk fluctuations and provide a concrete step toward computing correlators in confining gauge theories via holography, while highlighting the dictionary and renormalization challenges that remain in non-AdS settings. The framework offers practical tools for probing UV and IR dynamics, operator mixing, and the role of non-perturbative condensates in holographic duals of confining gauge theories.

Abstract

We consider gauge/string duality (in the supergravity approximation) for confining gauge theories. The system under scrutiny is a 5-dimensional consistent truncation of type IIB supergravity obtained using the Papadopoulos-Tseytlin ansatz with boundary momentum added. We develop a gauge-invariant and sigma-model-covariant approach to the dynamics of 5-dimensional bulk fluctuations. For the Maldacena-Nunez subsystem, we study glueball mass spectra. For the Klebanov-Strassler subsystem, we compute the linearized equations of motion for the 7-scalar system, and show that a 3-scalar sector containing the scalar dual to the gluino bilinear decouples in the UV. We solve the fluctuation equations exactly in the "moderate UV" approximation and check this approximation numerically. Our results demonstrate the feasibility of analyzing the generally coupled equations for scalar bulk fluctuations, and constitute a step on the way towards computing correlators in confining gauge theories.

Figures (4)

• Figure 1: Bulk toy models used in the literature. In the hard-wall approximation, the bulk is exactly AdS, so couplings in the gauge theory do not run (represented by straight sides in the figure). In singular approximations, like the singular conifold, there is logarithmic running, but also a curvature singularity (represented by the black dot).
• Figure 2: Illustration of the exponential map.
• Figure 3: Krasnitz matching for a generic field $\phi$. The solution denoted $\phi_{\mathrm{mUV}}$ is regular in the IR, and analogous to our solutions below. The solutions are matched to approximately agree in the cross-hatched overlap region.
• Figure 4: Moderate-UV analysis: comparison of the analytical solutions \ref{['KS:flucsols3']} of equation \ref{['KS:eqmotz']} with the corresponding numerical solution of \ref{['KS:eqmot3']} found by shooting (marked by crosses) for $k=10^3$, $P=1$. The "response functions" agree to an accuracy of 8%.