Duality Workshop: A Math-Physics Collaboration

Coordinators: Ron Y. Donagi, Albrecht Klemm, Burt Ovrut, Eric Zaslow

The Duality Workshop: A Math/Physics Collaboration, is a four week program to be held at the Institute for Theoretical Physics of the University of California, Santa Barbara from June 18-July 13, 2001. The program will focus on the interplay between physics and mathematics in string and M-theory, aiming to create an atmosphere mutually beneficial to members of the two communities. There will be a series of short courses on specific topics, interspersed with specialized seminars. The short course lecturers, and the titles of their mini-courses, are

    Week 1, Tuesday 6/19 - Friday 6/22:

      Ashoke Sen: D-Branes as Solitons
      Dan Freed: The Geometry and Topology of p-Form Gauge Fields

    Week 2, Monday 6/25 - Thursday 6/28:

      Paul Aspinwall: D-Branes on Calabi-Yau Varieties
      Greg Moore: D-Branes, RR-Fields and K-Theory

    Week 3, Monday 7/2 - Friday 7/6:

      Discussion groups and informal seminars

    Week 4, Monday 7/9 - Thurday 7/12:

      Mark Gross: Geometrical Approaches to Mirror Symmetry
      Hiraku Nakajima: Equivariant K-theory of Moduli of Sheaves on ALE Spaces


The emphasis of the workshop will be on combining the resources of mathematicians and physicists to better interpret and explore geometric concepts and the dualites originating in string theory, M- and F-theory and quantum field theory. These developments offer new insights into the structure of string theory at strong coupling, which may ultimately lead to a better non-perturbative formulation and improved phenomenology. Mathematically, they have spawned new invariant quantities in differential and symplectic/algebraic geometries; novel techniques for computation; and new categories. The joint effort at the workshop should help to sharpen the definitions of these subjects and to explore more of their physical and mathematical consequences.

Most notably, the following dualities stand at the fore: mirror symmetry; heterotic-type II and field theory dualities; heterotic-M-theory and heterotic-F-theory dualities; and the AdS-CFT correspondence. These represent not only new views of physical theories and their phenomenologies, but new connections between the mathematical objects they employ. Scanning these dualities, one easily arrives at a list of relevant mathematical topics: Gromov-Witten theory at higher genus and/or with boundaries; derived categories and symplectic(Fukaya) categories; special-Lagrangian submanifolds and fibrations; new integrable systems; spectral curves and G-bundles over fibrations; Seiberg-Witten invariants. In addition, there are a number of geometric concepts that are directly relevant to important physical issues. These include supergravity solutions and superconformal algebras; K-theory of non-BPS solitons; construction of holomorphic bundles subject to topological constraints. Some physics counterparts are: nonperturbative mirror symmetry; Yukawa couplings and effective actions; D-brane and boundary state couplings, and moduli spaces; BPS state counting in M(atrix) theory and F-theory; string vacua and supergravity compactifications; construction of realistic particle physics vacua.


During the first two weeks of the workshop, corresponding to the overlap period with the M-theory program, and also during the last week, there will be two mini-courses per week, each 4-6 hours in length. These courses will cover the most up-to-date topics in Math/Physics, such as K-theory, mirror symmetry and bundle theory, each taught by an expert in the field. These courses will be interspersed with specialized seminars covering an unrestricted range of topics. In the holiday shortened third week, we will be less formal, holding discussion groups and informal seminars on particularly interesting, new and "hot" topics. Throughout the workshop we will try to initiate new Math/Physics collaborative research efforts through such discussions.