Supersymmetric geometries

Lead Research Organisation: University of Edinburgh
Department Name: Sch of Mathematics


The project aims at the exploration, construction and classification of supersymmetric backgrounds of supergravity
theories and/or geometries admitting rigid supersymmetric field theories. The techniques in both problems are are taken
from spin geometry and representation theory. At a more concrete level, the problems consist in determining those spinor
equations on lorentzian spin manifolds (perhaps with additional data) whose solutions generate a Lie superalgebra and
then to study the class of Lie superalgebras which can be so constructed. Possible lines of study which follow from this are
the study of the representation theory of those Lie superalgebras with an aim at constructing supersymmetric quantum
field theories on those geometries and deriving new localisation results.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509644/1 01/10/2016 30/09/2021
1937590 Studentship EP/N509644/1 01/09/2017 31/08/2021 Ross Grassie
Description So far, this project has contributed two substantial papers to the Journal of High Energy Physics, both of which follow on from earlier work by Figueroa-O'Farrill.

The foundational work aimed to classify the spacetime geometries in which the laws of physics hold. Figueroa-O'Farrill achieved this classification by identifying the objective as a "physical avatar" of that which lead to Klein's Erlanger Programme, where geometries are associated with the group which acts on them. In the physical context, this group is called the relativity group.

The first paper produced by this project gives a systematic determination of geometric objects on the classified spacetime manifolds. These objects help to describe the dynamics of physical objects in these spacetimes.

The second paper extended the classification of spacetimes in four-dimensions to spacetimes in four-dimensions that admit supersymmetry. The inclusion of supersymmetry is motivated by its many applications in the generation of new theories of quantum gravity.

The combination of these works leads to exciting new research avenues for the incorporation of supersymmetry in particular condensed matter systems, the physics of objects going close to (or at) the speed of light, and gravitational waves. In particular, it introduces new geometric structures to aid in the development of physical theories which could lead to a working theory of quantum gravity.
Exploitation Route The outcomes of this research can be used by mathematical physicists to develop better models for certain condensed matter systems and gravitational waves.
Sectors Other