Supergravity Solutions for Branes Localized Within Branes

TL;DR

Explicitly constructing near-core, fully localized brane intersections in supergravity, the paper derives D2 branes localized within D6 branes and NS5 branes localized within D6 branes, starting from eleven-dimensional M-theory backgrounds and reducing to type IIA on a circle in the S^3 transverse space. The authors then use T- and U-duality to generate additional localized configurations, including a string localized on a 5-brane, and discuss the corresponding near-core harmonic-function structures (e.g., a $1/r^6$-type decay for the localized D2 in D6). The results provide analytic, near-core backgrounds that illuminate localized excitations on brane stacks and their dual descriptions (e.g., D0 on KK-monopole, F1 on D5), with potential implications for gauge/gravity duality and brane dynamics. Overall, the work demonstrates a systematic route to explicit localized intersections in M-theory and type II string theory and highlights the role of Z_N identifications and dualities in linking seemingly disparate brane configurations.

Abstract

We construct supergravity solutions describing branes (D2-branes or NS5-branes or waves) localized within D6-branes in the region close to the core of the D6-branes. Other similar string-theory and M-theory `near-core' localized solutions can be found by applying U-duality and/or lifting D=10 solutions to D=11. In particular, the D2-branes localized on D6-branes is T-dual to a special case of the background describing (D)strings localized on (D)5-branes and thus is also related to a localized intersection of M2-branes and M5-branes. D6+wave configuration is U-dual to a D0-brane localized on a Kaluza-Klein 5-brane or to the fundamental string intersecting a D5-brane with the point of intersection localized on the D5-brane.