After way too many months of work, I just sent my latest paper up to the archive. (Not accessible to the public yet; it’ll be available starting Sunday night)
The basic result:
In string theory (type IIA string theory, to be precise) there exist certain higher-dimensional objects called D-branes, whose important dynamical property is that strings (the basic objects of the theory) can end on them. (Normally strings are little closed loops; there can also be open loops if the ends are on these D-branes. Closed strings behave like gravitons, open strings behave like photons and gluons and other force particles, and their endpoints on the D-brane behave like matter particles such as electrons and quarks) In type IIA string theory, these exist in even-dimensional variants: There are point particles (D0-branes, 0-dimensional) membranes (2-d) and so on up to 8-dimensional branes.
It’s been known for some time that certain collections of D0-branes can form a membrane: because of their interactions (imagine strings stretched from one D0-brane to another) they develop a tension, and fluctuate like a single membrane. This membrane is known to be the same as the D2-brane. (So you can think of a D2-brane as a bound state of a bunch of D0-branes)
My research was examining the most general configuration that can show up as a bound state of (infinitely many) D0-branes. The answer turns out to be that all of the ordinary branes (Dp-branes for p even) can be thought of as bound states of D0-branes. In addition to these, there seem to exist “exotic” branes which don’t fall into this usual category: Strings can end on them (like ordinary D-branes) but they have more complicated dynamics, their shapes being described by noncommutative geometry. (Which is kinda hard to explain – think of the points of space “fuzzing out” into patches in an irreducible way)
And, after something like 9 months on this, it’s finally ready to go. Submission to a journal (Phys. Rev. D) for peer review the moment it’s up on the web…