Mathematics and Applications of Branes in String and M-theory

Organisers: Dr DS Berman (Queen Mary College, London), Dr JP Conlon (Oxford), Professor N Lambert (CERN/Kings College, London), Professor S Mukhi (Tata Institute, Mumbai) and Professor F Quevedo (Cambridge/ICTP, Trieste)

Programme Theme

M-theory is an 11-dimensional quantum theory of gravity which, in addition to gravitons and other particle-like excitations, includes extended objects known as membranes and five- branes. Though a complete definition of M-theory is not yet known, it is proposed as a nonperturbative formulation of superstring theory and as such is a compelling candidate for a unified theory of the fundamental particles and forces in Nature. Much has been learned about M-theory through its symmetries and its relation to supergravity and string theory and this has in turn led to important results in superstring theory and quantum gauge theory.

The nature and interactions of branes are key topics in string- and M-theory. Recently, quantum field theories to describe interacting membranes in M-theory have been proposed based on three-algebras and have led to exciting progress. On the phenomenological side, many particle physics models have been constructed using branes. However, key problems in the mathematics of multiple membranes and five-branes, as well as in the use of branes to model the real world, remain unresolved.

The basic themes addressed during the workshop will include:

• String/M-theoretic geometry: properties of compactifications, classifications of solutions, dualities and their uses e.g. T-folds and U-folds, fermionic T-dualities and the incorporation of p-form fields to give novel effective geometries.
• String/M-theoretic novel algebraic structures: Three-algebras, duality groups and higher exceptional groups such as E₁₀ and E₁₁
• Brane physics: Quantisation of branes, field theories for multiple branes and their intersections. Attempts to define a fundamental theory of membranes.
• Applications to strongly coupled field theory: The use of brane physics and the associated gauge/gravity duality for applications to strongly coupled systems such as nonperturbative quantum field theories and condensed matter systems etc
• Applications to particle physics: The role of string compactifications in string phenomenology, brane constructions of the Standard Model and the combination with supersymmetry breaking.
• Applications to Cosmology: The dynamics of branes in order to study early universe cosmology.

International Advisory Committee: Prof. J Harvey (Chicago), Prof. C Hull (Imperial), Prof. D Luest (Munich) and Prof. A Sen (Harish-Chandra)