Wow.

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)

hep-th/0210175

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…

Yipee!

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A question completely out of my depth:

Do the exotic D-branes have any particular implications as to what sort of gauge theory they’d imply?

This question may not make any sense whatsoever, and may be a case of me knowing just enough to ask really dumb questions. 🙂

Congratulations! I know you’ve been working on this paper longer than I’ve known you. *hugs* Now, you can sit back and relax for a few breathes before you start all that post-doc stuff you’ve mentioned to me. 🙂

Actually, the question makes perfect sense. An exotic brane is specified by a pair (A,X), where A is an algebra of functions on the brane (generalizing C(M) for a manifold M) and X is basically a set of gauge-covariant derivatives. The dynamics of open strings on these branes is given by a U(N) gauge theory on this noncommutative space. From a calculation perspective, this is the same as a commutative-space gauge theory whose gauge group is U(N)*D(A), where D(A) is a certain infinite-dimensional gauge group depending on A.

wow! congrats! [insert intelligent response to stuff i don’t know about here] 🙂

Ack! As I read this, I found myself unconsciously reaching for a pencil and paper, and thinking, “Damn, this is going to be one hell of a problem set! I don’t think we covered this in lecture…” And then I remembered why.

Congratulations! I know how much of a weight this has been, and I’m very glad to see you done with it and with something to show for your effort.

*wince* Man… we’re back to feeling stupid again.

Here’s a couple semi-silly layman questions, trying to relate this to something… or something like that (he mutters and trails off incomprehensibly)…

– What is the magnitude difference between D-branes and, say, an electron? I assume that “behaves like” is a reference to their properties as a mental model, not to any correlation with the larger objects? (this I hope is sort of a duh)

– What does “exotic” branes mean? As in, are they something that comprises “normal” matter but are somewhat strange, or does the “exotic” imply that they only occur in unusual circumstances (e.g. where some aspect of gets close to some sort of asymptote)?

– Do these branes go through state changes in their relationships to each other, or are they static? E.g. you refer to ordinary branes as bound states of D0-branes, but do they go through state changes from one to the other?

Umm, yeah. I have no idea what I’m talking about, really, but I’ll ask anyways. 😉

And, massive congrats! ^_^

What is the magnitude difference between D-branes and, say, an electron? I assume that “behaves like” is a reference to their properties as a mental model, not to any correlation with the larger objects? (this I hope is sort of a duh)The D-branes are actual particles… the D0-branes are just very heavy particles and don’t show up physically very often. Some higher ones may actually be the stuff that space is made of: There’s a 3+1–dimensional brane (a D3-brane) in type IIB string theory. Strings attached to the brane behave like photons and gluons and so on; the endpoints of these strings behave like quarks and electrons and so on; and circular strings (with no endpoints) that bump in to the brane behave like gravitons. So the world we see may actually

bea D3-brane…What does “exotic” branes mean? As in, are they something that comprises “normal” matter but are somewhat strange, or does the “exotic” imply that they only occur in unusual circumstances (e.g. where some aspect of gets close to some sort of asymptote)?The exotic means that they’re different from the ordinary D-branes, mostly because the geometry on their surface is noncommutative. (If we were to live on one of these in the same sense that we may live on a D3-brane, the actual geometry we would experience would be like that, and therefore very strange. But they’re still interesting because there can be branes within branes; we could live on a D3-brane and have a 2-dimensional exotic brane flying around somewhere and hitting people.

Do these branes go through state changes in their relationships to each other, or are they static? E.g. you refer to ordinary branes as bound states of D0-branes, but do they go through state changes from one to the other?I think that they do, and that’s one of the exciting things about all of this. The exact rules for how they can fuse and so on are actually really complicated, and that’s something I’m still trying to understand; in this paper I focused on the rules for two identical branes coming into contact, which is important for analyzing whether or not these things are stable. You can definitely take a bunch of D0-branes and build things out of them.

Sorry… he asked a technical question and got a technical answer. 🙂

Told you you could do it! 🙂 [big hug] And now . . . the Universe! Mwah hah hah!