## Monday, April 26, 2010

### Fuzzballs can melt wound strings

Stefano Giusto and Samir Mathur have a nice preprint today,
Unwinding of strings thrown into a fuzzball
that gives a pretty specific description of the way how black hole microstates can manage to spread the electric and magnetic fields, as dictated by the membrane paradigm.

Even individual microstates of a two-charge D1-D5 black hole, the fuzzballs, are apparently able to dilute the winding number of a string. The fuzzball contains a special curve inside the black hole, "S", whose location depends on the microstate and where the radius of the circle on which the string is wound is always shrunk to zero.

The spatial portion of the geometry near "S" resembles a Kaluza-Klein monopole while the temporal part is different - among other things, the "g_{tt}" redshift factor goes to zero. When a piece of an F-string approaches the curve "S", it can unwind over there and the corresponding flux quickly dilutes all over "S".

This is similar to the process in which F-strings absorbed by D-branes transform into the electric field within the D-brane. However, in this case, we have an apparently local, nearly non-singular description of the process for individual microstates.

I am actually confused by many details - starting from the very type of various fluxes whose fate gets modified - the authors use several pictures that are dual to each other and it is often difficult to figure out which picture is relevant for a given sentence.

And I am also confused about the possible speed of the spreading of the winding number along "S". Is the speed-of-light universal cosmic speed limit obeyed? But because "g_{tt}" goes to zero, this limitation may become arbitrarily vacuous near "S".

U-folds - non-geometric objects completing the multiplets

A week ago or so, Jan de Boer and Masaki Shigemori published a paper called
Exotic branes and non-geometric backgrounds.
They ask where all the charged states in M-theory on T^8 - or type II string theory on T^7 - come from. There are 128 scalars in maximally supersymmetric 3D supergravity. All of them may become gauge fields by the 3D electromagnetic duality.

But there are 240 different charged particles - many more. So the remaining 112 must be "exotic": this discrepancy doesn't occur above 3 large spacetime dimensions. The resolution is that for codimension 2 objects, you don't describe the charges fully by some U(1) integers: you need to know the whole non-Abelian monodromy.

Recall that there are (p,q) strings in type IIB string theory but to classify 7-branes, you need to know the full SL(2,Z) monodromy.

It's similar here. The authors kind of classify the monodromies and say where the exotically charged states come from in the decompactified string/M-theory: they come from U-fold where the trip around a circle of the torus induces a non-trivial U-duality.

Such objects are "globally non-geometric" but they can still be said to be "locally geometric".