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January 29, 2003


Dan Kabat was visiting today, and gave a talk about his work with Easther et al on M2-brane cosmology. I’ve commented on this before, so I thought I’d add what I further learned from my conversations with Dan.

One thing that confused me was their restriction a rectangular torus and to branes with wrappings parallel to the coordinate axes. Choosing a rectangular torus makes the computations much simpler (fewer parameters in the metric). The motivation for the latter is that “diagonally-wrapped” branes would not be compatible with maintaining a rectangular torus.

This is unfortunate, because the diagonally-wrapped guys are secretly rather important in the Brandenburger-Vafa type argument. It is only strings (branes) which are transverse which generically will intersect (and then, only if there are sufficiently few “large” dimensions). So the generic annihilation process is something like a (1,0) string and a (0,1) string annihilating into a (1,1) string.

Diagonally-wrapped strings (and hence, when we consider the back-reaction, non-rectangular tori) are inevitably going to occur. Brandenburger and Vafa never worried about the details of this. They merely noted that, even tranverse strings will generically never meet in more that 3 large spatial dimensions.

The other thing which vexed me in my original post was the non-semiclassical nature of the M2-brane, which made me wonder whether the naive picture of a gas of free branes could ever make sense (unlike a gas of free strings). If the branes are widely separated, then the “dressing” of the branes by those narrow throats simply represents the interaction of the branes with supergravity. Unlike the string case, there is never a “free gas” limit in which the coupling to supergravity can be made small (so I still don’t know how to do thermodynamics).

When the branes are not widely separated, of course, all bets are off. But, at least when some of the dimensions get large, we are “safe”, so long as we replace these “membrany” effects (to coin a phrase) with the coupling to supergravity.

Anyway, I’m a little clearer on what they’re trying to do so, on that score, Dan’s visit was a resounding success.

Posted by distler at January 29, 2003 12:38 AM

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