Unquenched flavor in the gauge/gravity correspondence

TL;DR

This review surveys how unquenched fundamental matter is incorporated in gauge/gravity duals using smeared flavor branes, focusing on the Veneziano limit where $N_c,N_f\to\infty$ with $N_f/N_c$ fixed. It develops a systematic framework (SUGRA+BIWZ) to compute backreacted backgrounds, derives BPS equations via kappa-symmetry, and applies them to a spectrum of models including AdS$_5\times X^5$, KS, and (2+1)D/QCD-like theories, illustrating beta-functions, Seiberg dualities, meson spectra, and quark-gluon plasma thermodynamics. Key results include analytic backreacted solutions for massless and massive flavors, controlled approximations in the small flavor parameter $\epsilon_*$, and predictions for observable quantities such as the meson spectrum shifts, jet-quenching, and speed of sound in flavored plasmas. The work demonstrates that smeared-flavor constructions capture essential IR physics and RG behavior while remaining tractable, enabling quantitative comparisons with field theory expectations and phenomenological insights. It also discusses limitations, such as UV Landau poles and IR singularities, and sketches future directions for more general embeddings and non- smeared setups. Overall, the framework provides a coherent, versatile toolkit for exploring strongly coupled gauge theories with dynamical flavors via holography.

Abstract

Within the AdS/CFT correspondence, we review the studies of field theories with a large number of adjoint and fundamental fields, in the Veneziano limit. We concentrate in set-ups where the fundamentals are introduced by a smeared set of D-branes. We make emphasis on the general ideas and then in subsequent chapters that can be read independently, describe particular considerations in various different models. Some new material is presented along the various sections.

Figures (9)

• Figure 1: Diagrams for a meson propagator, with two insertions of the meson operator ($n=2$) shown as thick points on the boundaries. The dashed lines are gluons that fill the diagram in the large $N_c$ limit and the thick lines are quarks. A) Planar diagram with no internal quark loops ($h=0$, $w=0$), the scaling is $\sim 1$. B) Planar diagram with an internal quark loop $h=0$, $w=1$, the scaling is $\sim N_f/N_c$. C) Non-planar diagram with no internal quark loops $h=0$, $w=0$, $b=2$, the scaling is $\sim 1/N_c$.
• Figure 2: On the left, a point-like charge (in red) and two lines of charge at different angles. On the right, a configuration with many lines of charge. In the asymptotic limit of an infinite number of lines, they just correspond to a radial charge density. This picture depicts an analogous situation to the case of smeared flavored branes, when the fundamental fields are massless.
• Figure 3: These pictures depict analogous situations to the case of flavored branes, when the fundamental fields are massive. On the right, again, we add a large number of lines, such that in the limit radial symmetry is recovered.
• Figure 4: We see on the left side the two stacks of $N_f$ flavor-branes localized on each of their respective $S^2$'s (they wrap the other $S^2$). The flavor group is clearly $U(N_f) \times U(N_f)$. After the smearing on the right side of the figure, this global symmetry is broken to $U(1)^{N_f - 1}\times U(1)^{N_f -1} \times U(1)_B \times U(1)_A$.
• Figure 5: The function $H$ in the massless-flavored KW model at zero temperature.