Monday, July 14, 2008

A watch at the string landscape

Like many physicist I am a reader of science fiction. String theory is not a topic which is too broadly covered in SF, and, anyway, it is not covered too properly. For example, it could be that the author limits to cite the words "calaby-yau" as some kind of manra. Even thought there is one particular novel, writen in the eiguthies, where there was a fine usage of string theory. There an alien spae-craft arrived to earth and they tripulants beguined a discusion with relevant human figures in art, politics an scince. In paarticular, in the sicence area, they tolked with string theorists and discused with them many mathematical aspects and conceptula developments that they found terribly exciting. Despite that no concrete experimental evidence was provided. While doing that the aliens had throught a black hole inside the earth which growed slowly, but fast enought to eat the whole earth a few mounths later, toward the end of the novel. Fortunately anonther space-craft had appeared, tripulated by a diferent alien specie, and saved some selected humans. I guess that any informed reader will be able to see the possible funny possible analogies with the actual situation :-).

The purpose of this introduction was to sign the fact that string theory has grown a lot in many directions since the eighties, and it is somewhat discouragint to try to get a prcise idea of the many lines (some of them alsmost death) of development followed in the while. But if I wuld be one of the "bad aliens" that would try to give some guidance to an eighties string theoretic maybe I could use this post as a begining, or at least that is my intention.

The great chalenge in string theory is to get a proer way to get a decent way to go from 10 to 4 dimensions. In the eighties the most pomising way was to look for compactifications of heterrotic string theory in calaby-yau mamifolds, or maybe in orbifolds. Soon it as realized that it was interesting to study not one, but families of calaby-yaus. One went from one to other by variiying some moduli. Another easy way to compatify were orbifolds, tori acted by some discrete group. The fixeed points of that action were singular, and the studie of that singularities revealed to be very interesting. It was necesary to go troguht a revolution, the discovering of the importance of branes, to give more fuel to the compactifications. One could use branes to solve the singularities of the orbifold fixed points. And it was found that that pints could do transitions among calaaby-ayus with diferent topologies. Also the Calabi-Yau moduli space revealed to hae singular points, called conifold points. Coriosly the own moduli space of a C-Y could be, in some sense, characterized a calaby yau of an special type, one with conifold points (i.e., a point similar to the edge of a cone, that is, a continuous but not diferentiable point). If one suits a D-Brane at that point one can "blow-up" the singularitie. But, anyway, the thing is that conifolds can also give transitions betwen vacua of diferent topology. In fact the scenarie is worst. Ther ecan be transitions to phases where the vacua doesnt´admit an obvious gemoetric description and one must use CFT/non linear sigma models, to describe the theory. In fact Witten argued that in M-theory, an aditional development of string theoyr corresponding to strongly coupled type II A strings, only geometric phases were allowed.

In adition to compactification "braane worlds" were considrd. The idea was that the observable world would be some kind of brane. Precise realizations of that idea were purchased form many viepoints (I guess that the most recent try use the idea of intersecting D6-Branes).

In the mean time it was discovred that the universe is accelerating. And there are som kind of consensun that at a constant rate. That means that "phantm energy" scenaries seen to be ruled out and we must look for a de sitter universe emerging from string theory. The firs realization of this was the KKLT theory. In that scenarie there were required vacuums where supersymmetry was broken in a way that it gived some cosmological constant. It was argued that the univrse could be populated by manu diferne vacua. Each vacuawith a diferent value of the cosmological constant would expand at diferents speeds so we would live in some buble of a particular vacua. That lead to the counting of vacua that shrd some properties, and to do an analisys of the statistical distribution of other properties. For example, in some kind of vacua compatible with aa certain value of the cosmological constant there were more solutions with large extra dimensions. But another kinds of such vacua ere in the opposite direction. By the way, vaua with cosmological constants are not tru vacuums, they are metastable states whose decay rate is graater that the actual ge of the universe, oh yeah ;-).

Some interesting remarks about this models are that they give a potential for the scalar fields that describe the moduli of the vacuas. Taht is, they re, in a certain sense, properly defined theories with all the measurable values fixed. This had proved to be a very difcould task. The Dine-Seiberg conjecture stated that a proper determination of the value of the modulis required to go to non-perturbative range of string theory. But the hope was that once one had a theory with aall that values fixed one would have a unique, of almost unique, theory. In fact one has, in some scenaries, around 10^500 theory (i.e. vacua). whose average cosmologicla constant is the observed one (the counting was made by first time by Bousso and Polchinsky for some particular kind of models). Another point is that there is not a natural way to make statistic mechanic for that diferent vacua. I.E, Ine can´t make a proper statistichal ensmble out of them because that vacua should be separated into diferent sectors with superselection rules not allowing going from one to another. I recmend to llok at the blog of Dimityr (non equibrium net) to get a mch better discusion of this topic.

By the way. Most of this studies were made for type II theories. What was of the hetrotic string?. Well, infact there is an heterotic landscape also. It is courious. Another development of string theory was to prove a counting of the benckenstein entropy of a black holes (or at least a paarticular kind of them). for that puropose Type II theories, and their D-Branes, were used. But later it was seen that one also could use heterotici strings to describe black holes. It seems like if heterotic string theory always has aa delay in the achievement of the resoults. But, in the positive point, heterotic strings still seem to be promising. FOr example teh heterotic landscape contians many fewer vacua.

In the eighties ther was a hope that string field theory could provide some kind of dynamics which could indicate how these compactifications could be achieed. Unfortunately string field theory had not succes and has proved to be very dificoult anyway. I fact one would have an string field theory fo rany of the diferen string theories.

With all that I have exposed it looks like if there are too many things going on. In fact it is so. I think taht what I would like to see is a way to see how topologicla transitions could be used to connect diferent vacua. In fact the vacua of the landscape aare, as I said, not aall of them supersymmetric vacua. That would mena to consider a more generic king of compactifications, and studie the possible topologicla transitions betewem them. One way to consider taht could be the use of instanton/euclidean wommholes. And also to see how to describe this in some kind of SFT. Also it one consider that the diferent string theories are related by dualities, meaning that in some sense they re a single one, one could study wormholes, ot whatever, connecting them. A way to beguin this program could be to try to describe some kind of wormhle like solution connecting diferent compactifications (or a noncapctifed space to a compactified one).

I muist advertize that like this post contain many, many, topics, I have not pretended to be very exact in the descriptions. My idea was just to give a broad perspective. I hope to wite in a near future more detailed posts on more concrete topics, but I guess it was too much tiem since the last posts and that It was a good idea not to bee too lazy and write smething ;-).