Fast strings

When I explain strings to non-stringy physicist, I often start out by stating that a string is like a rubber band and has a potential energy which is proportional to its length (like a 'relativistic Hook law'). Then, all you have to do is to covariantize this statement and you arrive at the Nambu Goto action.

You can, of course read this backwards: A string with potential energy E has a length proportional to E. Now, you can often read this as an explanation of why hard string scattering behaves much better than hard scattering of particles: At high energies, the strings in fact expand and thus the interaction delocalizes.

This, however, is only semi-true: I would think of what you have in hard scattering are strings which have been accelerated so that they have large centre of mass energy. But the centre of mass energy is decoupled from the internal energy of the oscillators and thus a boosted short string will still be short although it has large (kinetic) energy. On the other hand, you can have a long string with zero kinetic energy which just happens to be very heavy. So, in general, heavy strings are long, not fast ones.

So far, this is just kinematics, but can we see this in practice? What happens to a string that runs through a linear accelerator? So, the set-up would look as follows: You start with a string which is in a low mass state which is charged under some U(1) (maybe in a KK type theory, D-branes are welcome as well). Now it feels a electric field strength (of some cavity say). This electric field is a condensate of low energy (given by the normal frequency of the cavity) photons. So, you have to compute the scattering of the string with lots and lots of low energy strings in the vector field state.

Question: Even if the individual photon has energy much less than 1/sqrt(alpha'), does this scattering excite any of the higher oscillator modes (which make the string grow)? A Feynman diagram would look somewhat like

e----x-----x-----x-----x- ... -x-----h
     |     |     |     |  ...  |
     A     A     A     A       A

where e is the charged low energy state, A is the gauge field and h is a heavy state. Has this been done before?

Eurostrings

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.