Objective:

Outline of the scientific programme:

The mathematical framework for elementary particle theories consists of a quantum field theory described by a nonlinear generalisation of Maxwell's equations. The least understood part concerns the strong force responsible for the structure of sub-nuclear particles and is called Quantum Chromo Dynamics (QCD). The aim of the ASI is to assemble world experts in this field who can evaluate the impact of the latest developments, particularly those centred around electromagnetic duality, the main theme of the preceding programme. This concept involves the interchange of electric and magnetic fields. Its usefulness stems from the fact that it also interchanges weak coupling with strong coupling. Weak coupling means that reliable results can be obtained from the first few terms in a series expansion, whereas at strong coupling such a truncation does not make sense.

Recent developments have revealed the role of supersymmetry in making electromagnetic duality precise in a large class of theories. Roughly this is because supersymmetry facilitates cancellations between fermionic and bosonic fluctuations. The ASI will review the new knowledge and its relation to approaches in which supersymmetry is absent, in a way aimed at workers in QCD, at the level of an advanced graduate student or junior researcher. It will address the long standing question of understanding how quarks are confined within subnuclear particles. The intention will be to stimulate further activity and progress.

To be more specific, a good understanding of the running of the coupling constant, of the Wilson renormalisation group and of the particle spectroscopy will feature in a number of lectures, setting out the framework in which non-perturbative issues in QCD should be discussed. The renormalisation group will be discussed in the context of the lattice, momentum-cutoff and light-front approaches and will give the students working knowledge of the notion of effective actions and their flow under the renormalisation group. Introductory lectures on supersymmetry will prepare for the new ideas on electromagnetic duality. In the presence of supersymmetry, both instantons and monopoles will contribute in very special ways, revealing deep results relevant for the dynamics of the theory. This will be contrasted against what is known from the non-supersymmetric studies.

An important theme that will be developed in this context is the conjecture that monopoles condensate, such that QCD forms a dual superconductor. It will be discussed through the lectures how so-called abelian projection introduced ten years ago by 't Hooft might provide an explicit scenario to test this dual superconductor picture. The recent Seiberg-Witten duality results add a new dimension to this conjecture, whose consequence for QCD will be discussed as much as possible. Another line of attack, that might in interesting ways be related to the dual superconductor pictures, has been the attempts to rewrite QCD as a string theory. Also here supersymmetry recently has been shown to be a useful technical tool.

We are planning to roughly allocate equal time to four main themes, developed in parallel as illustrated in the enclosed tentative schedule, namely (i) duality in the light of its possible application to QCD, (ii) general non-perturbative techniques aimed at understanding confinement, (iii) the role of instantons and monopoles played in confinement, including tests of the dual superconductor picture and finally (iv) lattice Monte Carlo results aimed at first principle calculation of the consequences of QCD, like the glueball and hadron spectrum and the influence of the strong force on CP violation and electro-weak processes.

This ASI is unique in bringing so many different approaches together, each expected to carry part of the solution towards the confinement problem. Any student that wishes to make progress on the confinement problem should be aware of these approaches and the ASI will in particular stimulate exploring the ideas of electromagnetic duality to further our understanding of confinement in QCD.

This school aims at advanced graduate students and junior postdoctoral fellows and researchers.

Programme, Timetable and Organisation:

Check-in at Selwyn College with the Porter. Dinner is served at 19:30 for those who have signed up using the housing form. It takes 10-15 minutes to walk from the college to the Mill Lane lecture rooms. Follow Sidgwick Avenue, continue straight along Silver Street at the traffic lights. Across the bridge, with Queens College on the left, turn right into narrow Laundress Lane. This takes you to Mill Lane, turn left and continue for a couple of meters. The lecture rooms are on the right.

Organization

a.m. lectures: 9:30-10:30 and 11:00-12:00
p.m. lectures: 2:00- 3:00 and 3:30- 4:30

Seminars by visitors at the Newton Institute programme: 5:00-6:00 p.m. June 25-26 & July 1
Discussions with the lecturers: 5:00-6:30 p.m. June 27 & July 3
Poster sessions by participants: 5:00-7:00 p.m. June 24 & 30

Lunches can be taken any time between 12:15 and 14:00 at the adjacent University Center in the main dining hall. Vouchers will be provided upon registration.
Coffee and tea is provided during breaks between lectures (10:30-11:00, 15:00-15:30 and when appropriate 16:30-17:00).
Dinners are served 19:30 at Selwyn college (except for the banquet on Wednesday 2/7).

Schedule (ASCI version)

*** Registration from 8:30 at Mill Lane ***

a.m.

Gerard 't Hooft (Utrecht), opening lecture - Duality and oblique confinement

Chris Michael (Liverpool) - The glueball spectrum and string tension

p.m.

Gerard 't Hooft (Utrecht) - Duality and oblique confinement

Peter West (King's, London) - Introduction to supersymmetric gauge theories and duality