Supersymmetric webs of D3/D5-branes in supergravity

TL;DR

This work develops a Killing-spinor–based framework to study webs of D3- and D5-branes in type IIB supergravity, aiming to understand localized intersections and holographic duals of 3d N=4 theories. The authors construct a general supersymmetric ansatz with warp factors $H_1,H_2,D$ and a one-form $A_\alpha$, and introduce flux structures with $K=H_1^{-2}H_2^2$ and $H=H_1^4H_2^4$, yielding explicit expressions for the self-dual $F_5$ and the $G_3$ flux; the framework accommodates both localized and smeared D5-branes. Focusing on intersecting D3/D5 branes, they derive a nonlinear system for two functions, which simplifies in the smeared (semi-localized) limit to coupled equations for $H( ho)$ and $K( ho,r)$, and obtain exact asymptotics: in the far region $H o 1$ and $K o R_0/(r^2+ ho^2)^2$, while near D5 one has $H o q/ ho$ and $K$ given by $K = qQ/[ ho (r^2+4q ho)^{5/2}] + q/ ho$. These results clarify the geometric structure of D3/D5 webs and provide a practical setting to explore AdS$_4$ branes in AdS$_5$, though fully localized solutions remain to be found in future work.

Abstract

We study webs of D3- and D5-branes in type IIB supergravity. These webs preserve at least 8 supercharges. By solving the Killing spinor equations we determine the form of supergravity solutions for the system. We then turn to the sub-class of the intersecting D3/D5 brane system and elucidate some of its features.