Mesons in gauge/gravity dual with large number of fundamental fields

TL;DR

This work extends gauge/gravity duality to include fundamental matter beyond the probe approximation by analyzing the fully backreacted D2/D6 system, whose IR physics is a 2+1d ${\cal N}=4$ SU($N_c$) theory with $N_f$ fundamentals at a conformal fixed point. The authors establish a fluctuation-operator dictionary in the Pelc–Siebelink geometry, showing that meson-like operators with fundamentals correspond to closed-string supergravity fluctuations, and they compute the lowest-lying meson mass by solving the corresponding wave equation. They find a robust linear dependence $M \propto m$ of the meson mass on the quark mass, in agreement with field-theory expectations under SUSY, and they demonstrate a two-fold open-closed string duality that separates adjoint and flavour sectors. The results provide a concrete holographic framework for flavours at backreaction and suggest extensions to four-dimensional theories and connections to other holographic flavor phenomena, including potential links to the Witten–Veneziano mechanism and chiral dynamics in SUSY contexts.

Abstract

In view of extending gauge/gravity dualities with flavour beyond the probe approximation, we establish the gravity dual description of mesons for a three-dimensional super Yang-Mills theory with fundamental matter. For this purpose we consider the fully backreacted D2/D6 brane solution of Cherkis and Hashimoto in an approximation due to Pelc and Siebelink. The low-energy field theory is the IR fixed point theory of three-dimensional N=4 SU(N_c) super Yang-Mills with N_f fundamental fields, which we consider in a large N_c and N_f limit with N_f/N_c finite and fixed. We discuss the dictionary between meson-like operators and supergravity fluctuations in the corresponding near-horizon geometry. In particular, we find that the mesons are dual to the low-energy limit of closed string states. In analogy to computations of glueball mass spectra, we calculate the mass of the lowest-lying meson and find that it depends linearly on the quark mass.

Figures (6)

• Figure 1: Two-fold open-closed string duality: a) standard duality between adjoint operators (2-2 strings) and a class of closed strings. b) flavour string duality between meson operators (2-6 strings) and another class of closed strings. This will be discussed in detail in Sec. 3.1.
• Figure 2: Plot of $F(w;m=2)$ for different values of $y=\sin \beta \cos \frac{\theta}{2}$ ($\psi=0$). The step function $\Theta(w-m)$ is plotted just to guide the eye.
• Figure 3: Mirror symmetry.
• Figure 4: Self-energies of quarks represented by fundamental strings extending from the D2-branes and ending at infinity.
• Figure 5: The radial direction corresponding to the energy scale in the field theory. The dashed direction does not have an energy interpretation. The dotted arrow represents the direction which we have chosen for the meson computation and corresponds to the regularization ($\beta \lesssim \pi/2$).