Fuzzy Funnels: Non-abelian Brane Intersections

TL;DR

Constable, Myers, and Tafjord analyze dual descriptions of D3$\perp$D1 and D5$\perp$D1 brane intersections, showing that a D3-brane worldvolume picture with monopole/bion spikes and a D1-brane worldvolume picture with a fuzzy funnel provide complementary descriptions that converge in the large $N$ limit. They derive explicit solutions: the D3 picture yields $\phi=\frac{N}{2r}$ and a BPS bound $\nabla\phi=\pm\mathbf{B}$, while the D1 picture gives Nahm equations and a funnel radius $R(\sigma)$ matching the D3 geometry as $N\to\infty$, including RR couplings. Extending to D1 ending on D5, they construct a fuzzy $S^4$ funnel with $R(\sigma)$ transitioning from universal to harmonic behavior and show that the non-abelian WZ term sources $n$ D5-branes; the D5-brane instanton description matches the D1 funnel in the large $N$ limit over a broad regime. Overall, the work demonstrates robust duality between different-dimensional worldvolume theories for brane intersections, with implications for noncommutative funnels and extensions to other fuzzy geometries.

Abstract

We discuss dual formulations of D-brane intersections. The duality is between world volume field theories of different dimensionalities which both describe the same D-brane configuration but are valid in complementary regions of parameter space. We discuss the duality in terms of bion configurations involving D-strings orthogonally intersecting both D3-branes and D5-branes.