Isaac Newton Institute for Mathematical Sciences

Strong Fields, Integrability and Strings

23 July - 21 December 2007

Organisers: Professor N Dorey (Cambridge), Professor S Hands (Swansea) and Dr N MacKay (York)

Scientific Advisors: Professor L Alvarez-Gaume (CERN), Dr N Evans (Southampton), Professor T Hollowood (Swansea), Professor K Intriligator (UC San Diego), Dr M Teper (Oxford), Dr D Tong (Cambridge), Professor A Tseytlin (Imperial College), Professor P van Baal (Leiden) and Dr K Zarembo (Uppsala)

Programme Theme

Two central theories in modern theoretical physics are gauge fields and strings. Quantum gauge fields form the basis of the standard model of elementary particle physics, and are also rich mathematically - indeed, a rigorous derivation of their spectrum is one of the Clay Institute's seven millennium prize problems in mathematics. String theory potentially unifies quantum physics with gravity, and has offered a rich vein of mathematical exploration for over thirty years. Right from the early days, when string theory was envisaged as a model of strongly interacting particles, and more recently exemplified in the AdS/CFT correspondence, it has been clear that there is a close and rather mysterious relationship between the two.

The programme starts with some open issues in QCD, the gauge theory of quarks and gluons. Both conceptual issues such as dynamical mass generation and color confinement, and phenomenological ones such as properties of the quark-gluon plasma studied in ultra-relativistic ion collisions and the nature of matter at high baryon density, can be tackled by a variety of non-perturbative approaches involving lattice simulations, the properties of topologically non-trivial solutions of the Yang-Mills field equations, or random matrix models.We then consider more theoretical questions, in particular involving supersymmetry and large-rank gauge groups, where pure N = 1 supersymmetric Yang-Mills theories (SYM) are directly connected with QCD. The increased analytic control offered by such models coupled with new techniques based on duality symmetries have enabled many exciting new, exact results in recent years, including bounds on transport coefficients which may potentially inform RHIC phenomenology. The same ideas, for varying degrees of supersymmetry, naturally recur in matrix models and string theory, and lead on to the central theme of the programme, the gauge/string correspondence. A recent feature of this has been the ubiquitous appearance of 'integrability', the exact solubility of certain classical and quantum models. Integrability appears on both sides of the AdS/CFT correspondence, with spin-chain techniques enabling the calculation of anomalous dimensions in the N = 4 SYM which match string states which are those of classical integrable systems, while the hidden symmetries of the full AdS string sigma models are yet to be unravelled. Another important recent development is the reformulation of weakly-coupled Yang-Mills theory as a string theory in twistor space, leading to a resurgence in the application of string-inspired techniques to perturbative calculations in gauge theories.

The programme thus encompasses a broad sweep of interests and techniques, from strong-interaction phenomenology and lattice simulation through theoretical aspects of gauge fields and strings to integrability. In our view there has never been a more fertile time for workers from different ranges of this spectrum to interact and exchange ideas and insight. The programme will be supplemented by workshops on Deconfinement in QCD (in August) and Integrability and the gauge/string correspondence (December) and a school on Gauge fields and strings (September).

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