Brane Surgery

TL;DR

The paper introduces a simple, general 'brane surgery' approach that reads off Chern-Simons terms in $D=10$ and $D=11$ supergravity to determine when a $p$-brane can have a boundary on a $q$-brane and what the boundary carries on the $q$-brane's worldvolume. It derives explicit boundary rules for Type IIB, Type IIA, and M-theory: in IIB, the fundamental string can end on $D3$- and $D5$-branes and, via dualities, on a $D7$-brane; in IIA, the string can end on a $D4$-brane and the 2-brane on $D4$ or $D6$, with membranes mediating endpoints; in M-theory, the M2 can end on the M5, with the boundary appearing as a string on the fivebrane. The method emphasizes that CS terms encode non-perturbative boundary physics and reveals deep connections between brane boundaries, dualities, and worldvolume gauge dynamics, pointing toward a unified, CS-term–driven picture of brane interactions within M-theory. The analysis also highlights the interplay between perturbative and non-perturbative descriptions and suggests a path to understanding intrinsic M-theory beyond perturbation theory.

Abstract

Some aspects of the role of p-branes in non-perturbative superstring theory and M-theory are reviewed. It is then shown how the Chern-Simons terms in D=10 and D=11 supergravity theories determine which branes can end on which, i.e. the `brane boundary rules'.