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The Bethe Ansatz has over the years been extensively used for the description of the thermodynamics of integrable models. However, dynamical quantities such as space- and time-dependent correlation functions are not readily computed using these traditional methods. In this series of lectures, recent progress on this issue will be presented, with spin chains and interacting Bose gases as examples.
The idea of a solitary wave, or 'soliton', is rather old, stretching back to nineteenth century observations concerning the propagation of waves on shallow water. In fact, soliton behaviour occurs in many areas of physics and is starting to have a technological impact. Moreover, following Skyrme's work in the 1960s, solitons have been recognised as being important entities in quantum field theory, especially as sources of ideas and insight. Examples are skyrmions, magnetic flux tubes or magnetic monopoles; and the language of solitons has penetrated gauge theory, string theory and its generalisations.
Recent work has concentrated on the behaviour of classical solitons, or their quantum counterparts, in field theories defined on restricted domains and has led to a number of interesting, sometimes unexpected, new insights. The lectures will start with a survey and then specialise to some of the recent developments. The principal example will be provided by the sine-Gordon model, which arises in several physically realiseable systems. Possible areas for future developments will be outlined as the talks progress.
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Two-dimensional quantum field theory allows for a large class of exactly
solvable cases. These are the Conformal Field Theories, which describe the
critical points of statistical models, and the Integrable Field Theories,
which describe some directions in the scaling region around such critical
points. After recalling the characteristic features of Integrable Field
Theories, we will explain how they can be used as starting points for the
study of the non-integrable ones. The Ising field theory with magnetic
field and the multi-frequency sine-Gordon model will be used as main
examples to illustrate topics such as the interpolation between integrable
theories, confinement of topological excitations and particle decay.
From the short-wave limit of a model describing capillary-gravity surface waves in shallow water, we have found a new integrable equation with peculiar features such as solutions becoming singular in a finite time and Lorentz invariance. I will show how it is related to classical sine/sinh-Gordon model through a transformation of space-time and fields and present the rather unusual relativistic model we can build from this equivalence. I will discuss briefly some of the quantum aspects of the latter and the the problems that arise in the quantization. Finally, I introduce a generalisation of this new equation and its relation with usual integrable theories.
I review recent indications for the all-loop integrability of planar N=4 gauge theory, and compare to similar, parallel developments in the dual AdS string theory description. I discuss a very recent, first candidate for the gauge theory's non-perturbative dilatation operator in a sector of the theory: The Hubbard model. Finally I apply the integrability conjecture to the sector of twist operators, and find a novel all-loop scaling function for their large spin anomalous dimension.
This series of lectures will review the modern approach to building conformal field theories in two dimensions. Topics will include:
The gong show is a series of 3 minutes talks by all the participants. The duration of 3 minutes for each talk will be strictly enforced by a gong, so there cannot be any extra time. Possible questions will also have to be postponed.
Participants are encouraged to present one of their recent scientific results in a form which can be understood in 3 minutes. An easier (and less recommended) version is to generally explain what topic one is working on, and what one is trying to achieve.
Giving a 3 minutes talk requires a fair amount of preparation and possibly rehearsal. Transparencies can of course be used, but laptop presentations are forbidden for obvious reasons. A blackboard will be available, good luck to anyone trying to use it.
The concept of a gong show is not new, it was already put in practice at the Cargese school, and one participant even published a "gong-note" hep-th/0302043. (Out of frustration of not having had enough time for explaining the subject?)
The gong show is also a way for participants to introduce themselves and learn what the others are working on. It provides a unique opportunity for young researchers to talk at an international scientific meeting. But note that all participants (except possibly lecturers) are required to talk. It is particularly important that senior participants lead by example. Those who do not talk will have no dessert at the conference dinner.
For further information please contact: sylvain "dot" ribault "at" desy "dot" de.