I just came back from one week of

Eurostrings at DAMTP, Cambridge which was a combination of a network meeting of the EU String Network then turning into a celebration of Michael Green's 60th birthday. So, before anything else:

*Happy Birthday, Michael!*This was a particularly nice event and quite different from other european meetings there was also a large number of people from the Americas attending which I assume was due to a) celebrate Michael and b) that this year's Strings '06 conference in Beijing is not too attractive for a number of people for various reasons.

Once more, I was surprised how many people actually read this blog and came to me during the conference mentioning some of my entries in the past.

As here was no wireless network operational during the conference and unlike the Loops '05 I did not feel the strong urge to report. Victor Rivelles already

has and

Peter Woit has as well.

There were no really big surprises, just look at the titles of the talks and you get a pretty good idea what was going on; there are online proceedings for those who want more details. Looking through my notes reminds me of a few that are worth mentioning never the less: There were talks by Damour, West and Kleinschmidt about the relations between M-Theory and hyperbolic Kac-Moody algebras. By now, it becomes clear how this works dynamically (at least at low levels). The KMA structure even fixed numbers like the coefficient of the CS term in 11d sugra which is usually determined by supersymmetry. I would really like to see worked out how this works in detail, it would

not be the first time, there is a relation between exceptional Lie algebras and susy.

A number of people talked about the relations between spin chains and N=4 SYM and strings and another theme discussed by several speakers was the relation between black holes and topological strings (known under the names of OSV). Especially, Strominger gave a nice derivation on the blackboard of the mysterious square formula.

Seiberg gave two talks both quite interesting, the first on a paradox if you apply T-duality in the euclidean time direction to relate high and low temperature physics and how this is related to the Hagedorn transition and the second on his findings in N=1 theories which even if they have a vanishing Witten index often have a non-susy meta-stable state at the origin of scalar field space. This is potentially very interesting phenomenologically as it provides a mechanism of dynamical susy breaking but unfortunately I understand too little of N=1 gauge theories to give you more information. But you can read it all in the paper.

Finally, I would like to point out a little triviality in elementary quantum mechanics which seems not to be generally appreciated. Imagine that some degrees of freedom are not accessible to you, maybe because they are behind a curtain or even the horizon of a black hole. Formally, you write your Hilbert space as a tensor product

. The whole system is in a state described by a density matrix

which could well be a pure state

. As you see only part of the degrees of freedom, you observe only the partial trace

, where the trace is over

.

The time evolution is is given by the Heisenberg equation

and this implies that the entropy

does not change with time. Especially, a pure state (with entropy 0) cannot evolve to a mixed state and vice versa.

This however is not true for the reduced state

. It evolves unitarily as

only if the total Hamiltonian is a tensor product

that is if the two tensor factors of the Hilbert space do not interact.

Otherwise, for example if you throw stuff behind the curtain (or horizon) the time evolution of

is more complicated and

will change in time. This means, if we only observe part of the Hilbert space, a state that was pure in our part of the Hilbert space can become mixed by interactions with the other degrees of freedom.

This is of course well known to people working on decoherence but somehow not so much amongst people thinking about quantum cosmology.