The D3/D7 Background and Flavor Dependence of Regge Trajectories

TL;DR

This paper constructs a fully backreacted D3/D7 type IIB supergravity solution with a logarithmically running axion-dilaton, providing a warp-factor expression that encodes the positive beta function of the ${N=2}$ gauge theory with $N_f$ fundamental hypermultiplets. It excitively links the Landau-pole scale $\Lambda_L$ to the dilaton divergence and shows that logarithmic tadpoles reproduce the one-loop running of the gauge coupling, demonstrating a consistent unquenched holographic description. Using the decoupling limit and a classical spinning string, the authors extract flavor-dependent Regge trajectories $E(\sqrt{J};N_f)$, finding that larger $N_f$ lowers the energy for a given spin due to screening, while the string length remains unchanged. The work thus provides a concrete framework to study unquenched flavors in holography, enabling exploration of non-conformal dynamics and potential confining scenarios beyond the quenched approximation.

Abstract

In the context of AdS/CFT with flavor, we consider the type IIB supergravity solution corresponding to a fully localized D3/D7 intersection. We complete the standard metric ansatz by providing an analytic expression for the warp factor, under the assumption of a logarithmically running axion-dilaton. From the gauge dual perspective, this behavior is related to the positive beta function of the N=4, d=4 SU(N_c) super Yang-Mills gauge theory, coupled to N_f fundamental N=2 hypermultiplets. We comment on the existence of tadpoles and relate them to the same gauge theory beta function. Next we consider a classical spinning string configuration in the decoupling limit of the D3/D7 geometry and extract the flavor (N_f) dependence of the associated meson Regge trajectory. Including the backreaction of the D7-branes in the supergravity dual allows for going beyond the quenched approximation on the dual gauge theory side.

Figures (5)

• Figure 2.1: Plot of the near-core solution $y(\rho)=K_0(\sqrt{\lambda x e^{2x}})$ ($x=\log \rho/\rho_L$) and the exact solution $y(\rho)$ for $N_f=1$, $q=0.1$. The near-core solution breaks down around $\rho_L$.
• Figure 3.1: Example of a string profile $\tilde{z}(\tilde{R})$.
• Figure 3.2: Chew-Frautschi plot for $N_f=0,1,2,3,5, 10$ additional massless flavors. The straight line represents the $N_f=0$ trajectory for small spin values. All graphs approach the horizontal line $E=2m$.
• Figure 3.3: String length $R_0(J)$ for different $N_f$.
• Figure 3.4: String tension in dependence of the number of flavors $N_f$ for $J=0.4^2$ (upper graph) and $J=0.6^2$ (lower graph).