Beyond space and time

Research Project, 2016 – 2019

This is a project in the crossroads of physics and mathematics. The question of what quantum gravity is, and what lies behind the emergence of space and time is one of the central questions in fundamental physics. The project is motivated by the appearance of symmetries appearing in string theory and its more general framework of M-theory, in particular duality symmetries, which can give important clues concerning the nature of space-time. We will examine the consequences of the presence of these symmetries and implement them at a more fundamental level.

The project has three main themes:

A radical reconsideration and extension, in and beyond generalised and extended geometry, of the basic concept of geometry, generalising the use of Riemannian geometry in Einstein gravity. I intend to continue to systematically develop the basic concepts and the formalism of extended geometry, and to apply it to non-perturbative string theory by investigating solutions and non-perturbative states.

Supersymmetry, especially maximal supersymmetry, will be investigated, with the goal of finding a generalised supergeometry and its associated structures, analogous to pure spinors for ordinary supergeometry, allowing for off-shell formulations.

The connections to algebraic origins of space-time, such as hyperbolic Lie algebras and unfolding, will be investigated by extending the framework of generalised geometry beyond the dual gravity barrier, which may give significant progress in the understanding of string theory itself and of the nature of space-time.

These three themes are expected to be closely related, as is described in the project plan, and one aim of the project is in fact to develop this connection.

The methods used are thinking, discussions and calculations, mostly manual but with some assistance from algebraic and symbolic computer programs.

On an organisational level, the purpose is to set up a focused group of researchers with overlapping interests and agendas, a mathematical laboratory which will work it as a centre for international exchange and collaboration. The aim is to create a group of a modest size, which will be absolutely world-leading in the subject area. The group will have the potential to give a significant contribution to the understanding of M-theory / string theory, and may make good progress concerning finding variables for quantum gravity beyond time and space at a more fundamental level. The presence of the people will be a huge asset for the department, for Chalmers and for the Swedish theoretical community, and will also make a significant imprint in terms of international exchange. There is potential for advance in some areas of pure mathematics. The greatest added value in this kind of pursuit is as always to find in its rôle as a cultural activity. It is thus an ambitious, but extremely relevant and potentially very rewarding project. If successful, the project has the potential of shedding much new light on the non-perturbative nature of string theory and M-theory, and provide a window not only into non-perturbative physics, but also physics which is beyond the reach of traditional geometry. A partial success may already bring about much of this.

The feasibility is, as always in a theoretical project, hard to judge, but some of the more basic questions are clearly within reach, and promise to yield interesting results. Some of the more difficult questions I have raised may be harder to resolve, or may be resolved in other ways than I can envisage now, and it is likely that new questions and directions will emerge, which I am not in a position to describe now. The area seems mathematically very rich, and the risk of failure in the sense of running out of meaningful and relevant problems in a couple of years can most certainly be excluded. I would characterise the project as high-risk, but with a safety belt.