The two main goals of current work in fundamental physics are (i) to find a quantum theory of gravity that avoids the inconsistencies that arise from trying to reconcile Einstein's theory with quantum mechanics, and (ii) to find a unified theory of all the forces and particles of nature. Superstring theory provides a very promising candidate for a theory that could achieve both of these aims simultaneously. Recent discoveries have revealed that all five superstring theories arise as sectors of a single all-encompassing structure, which has come to be known as "M-theory". Much has been learned about those special sectors of M-theory which can be described by string theories or supergravity theories, and of the remarkable duality symmetries that relate such sectors, but much of M-theory remains a mystery. We have as yet no definition or formulation of the theory, and do not even know what the fundamental degrees of freedom should be. It seems likely that our notions of space and time will have to be modified, bringing in new mathematical structures such as non-commutative geometry, which has recently been shown to play an important role. An important clue has been found in the recent discovery that M-theory, at least in certain backgrounds, has a "holographic" description in terms of a simple non-gravitational gauge theory or matrix theory.
The principal aim of the programme is to investigate the structure of M-theory, with an aim of seeking its fundamental formulation. The main themes to be explored include:
- Branes, Geometry and Dualities. Geometry of M-theory solutions and their modifications due to branes; D-geometry and conformal field theory. Supersymmetric geometry and calibrations. Duality symmetries, particularly in cases preserving only a minimal amount of supersymmetry, and mirror symmetries. Non-BPS branes and K-theory. (2,0) theory in 6 dimensions and the non-abelian generalisation of anti-symmetric tensor gauge theory; little string theories. String field theory.
- Holography. Formulation of quantum gravity or M-theory in D dimensions as a non-gravitational theory in D-1 dimensions. Anti-de Sitter space and conformal field theory; matrix theory; general backgrounds and non-conformal field theories.
- Mathematical Structures of M-theory. Non-commutative geometry; quantum geometry and topology change; hyperbolic algebras, vertex algebras and exotic algebraic structures; K-theory.
- Quantum Gravity and M-theory. Implications of M-theory for key problems in quantum gravity. Black holes and microscopic origin of Beckenstein-Hawking entropy; singularities; information loss; cosmology; thermodynamics.
At the end of the Newton programme, the annual international conference in M/string theory will be held in Cambridge, 15-20 July; for information on Strings 2002, see www.damtp.cam.ac.uk/strings2002/