Friday, April 08, 2005

Lisa Randall's talk

Lisa Randall just spoke about the "inverse Brandenberger-Vafa" mechanism. According to Brandenberger and Vafa, the world has 3+1=4 large dimensions because 2+2=4. This may sound as a childish statement, so let me say a few more words about it.

The dimension of the worldsheet of a fundamental string is two. The maximal spacetime dimension in which two worldsheets generically cross - and allow the wrapped strings to annihilate (and unwind) which allows the space to expand - is "2+2=4", which is why we are supposed to live in four large dimensions. A larger number of dimensions can't expand because the strings would not have enough chance to annihilate (there is too much space and the strings have too a small dimension), and the remaining wrapped strings would prevent the small dimensions from expanding to astronomical sizes.

You might object that this argument also allows a lower-dimensional spacetime to develop, but 3+1 dimensions are preferred. If nothing prevents 3 spatial dimensions from expanding, it will occur.

There is a huge number of small problems and subtleties about this proposal, but it is undoubtedly attractive to imagine that a cosmological mechanism explains things such as the dimensionality of the Universe. Recently, in the context of the second superstring revolution, the Brandenberger-Vafa framework was upgraded to the "brane gas cosmology" which includes not only strings but also higher-dimensional branes.

Lisa's approach is the opposite one: she wants to consider the mutual annihilation of branes in a higher-dimensional Universe. Consider some simplified type IIB string theory. The branes with low dimensions won't annihilate too much, but the p-brane energy density will simply decay as
  • a^{p-n}
where "n" is the total number of spatial dimensions (nine). The higher dimension the brane has, the less rapidly its energy decays because its total volume scales like "a^p" where "a" is the linear size of the Universe. However, for 4-branes and higher, it is very likely that they will annihilate with their antibranes rapidly, and you must use a different power law. As Lisa combines the pieces, she argues that 3-branes and 7-branes are those that survive. A pretty good starting point for phenomenology. Except that one also needs 3+1-dimensional gravity, and Lisa argues that it is also possible to localize 3+1-dimensional gravity on a triple intersection of three stacks of some kind of 7-branes stretched in the usual SUSY way,
  • ++++__++++
  • ++++++__++
  • ++++++++__,
assuming that the bulk is something like AdS_{10} (a hard background to realize in type IIB). There may be many bugs and stringy subtleties that are neglected, but I definitely think that it's useful if Lisa provokes others to think about these issues.

Many formulae looked more concrete than last time when I was collaborating on this line of reasoning, and as Lisa says, this sort of Brandenberger-Vafa reasoning may be useful to identify a cosmological selection mechanism that will find some preferred vacua (in this case: braneworlds) within the landscape of possible vacua.

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