The D2-D6 System and a Fibered AdS Geometry

TL;DR

This work analyzes the D2 branes localized on D6 branes and their AdS/CFT dual, showing that the IR geometry can be a fibered AdS$_4$ over a compact base $X_6$ for an intermediate flavor-to-color ratio. The authors map the phase structure across 11D and 10D geometric descriptions, derive UV–IR relations, quark potentials, and entropy behavior, and demonstrate a smooth crossover rather than a sharp phase transition between regimes. They extend the analysis to off-D6 configurations and NS5–D6 systems, and connect the D2–D6 setup to related systems via compactification and dualities, reinforcing the consistency of the AdS/CFT framework for intersecting branes. Overall, the paper provides a detailed geometric and field-theoretic map of the D2–D6 system, elucidating how open-string degrees of freedom and quark dynamics arise and flow under RG transformations in three dimensions.

Abstract

The system of D2 branes localized on or near D6 branes is considered. The world-volume theory on the D2 branes is investigated, using its conjectured relation to the near-horizon geometry. The results are in agreement with known facts and expectations for the corresponding field theory and a rich phase structure is obtained as a function of the energy scale and the number of branes. In particular, for an intermediate range of the number of D6 branes, the IR geometry is that of an AdS_4 space fibered over a compact space. This D2-D6 system is compared to other systems, related to it by compactification and duality and it is shown that the qualitative differences have compatible explanations in the geometric and field-theoretic descriptions. Another system -- that of NS5 branes located at D6 branes -- is also briefly studied, leading to a similar phase structure.

Figures (2)

• Figure 1: The phase diagram of the world-volume theory
• Figure 2: Leading diagrams in the large $N$ limit. (a) large $\nu$; (b) generic $\nu$.