Generalised geometry of generic supersymmetric string backgrounds
Lead Research Organisation:
Imperial College London
Department Name: Physics
Abstract
Generalised geometry is a new approach to describing generic supergravity backgrounds that unifies the bosonic degrees of freedom and symmetries. The project will apply this formalism to understanding the properties of generic supersymmetric geometries. It is already known that these are equivalent to generalised integrable G-structures. A key questions are to describe moduli spaces of solutions. This has important implications for gauge/gravity duality, specifically the description of marginal deformations, and phenomenology, specifically the description of massless modes. It should be possible to use the ideas of general deformation theory to finding the DGLA underlying the problem, which also may have interesting mathematical implications. The dual gauge theory also provides an algebraic description of same geometry, which should correspond to some particular generalisation of complex algebraic varieties, perhaps a sort of non-commutative geometry. Finally, the DGLA description should correspond to degrees of freedom of some topological theory, generalising the conventional topological type IIA or IIB string, to include RR or M-theoretic degrees of freedom.
Organisations
People |
ORCID iD |
| Daniel Waldram (Primary Supervisor) | |
| David Tennyson (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| ST/N504336/1 | 01/10/2015 | 31/03/2021 | |||
| 1811186 | Studentship | ST/N504336/1 | 01/10/2016 | 31/05/2020 | David Tennyson |
| Description | String theory is a theory of quantum gravity and hence provides a possible model for gravity in our universe. We call the different gravitational backgrounds it models 'string backgrounds'. If they have a certain property that we call 'supersymmetry', we call them 'supersymmetric string backgrounds'. One can use geometric techniques to study these backgrounds and determine certain properties about them, such as the different fundamental particles we would observe and their interactions. Unfortunately, these backgrounds are very complicated and traditional geometric techniques are limited in their effectiveness for analysis. However, a new formulation, called 'generalised geometry' is ideally suited for studying completely generic backgrounds of string theory. The aim of this award was to use generalised geometry to study supersymmetric string backgrounds and their properties. We were able to analyse completely generic (N=1) supersymmetric backgrounds of both maximal strings and heterotic strings, and find their moduli. We were able to match our results to previous literature, as well as extend their results. This analysis uncovered new and interesting geometric structures that may enhance our understanding of string theory beyond the gravitational background. This includes the creation of 'exceptional complex structures', a property that all supersymmetric backgrounds hold. We began an analysis of a potential unbroken phase of string theory characterised by topological/geometric invariants of the gravitational background. In our analysis, we were able to frame old questions in conventional geometry in a new framework that may be admissible to the techniques of 'geometric invariant theory'. This is a powerful technique that has been used to solve many problems and mathematics. We may be able to use it to solve outstanding questions in geometry. |
| Exploitation Route | The new geometric structures and techniques that we have discovered will have important implications for string theory and mathematics. Firstly, string theory can predict universes with different properties depending on which additional data you put into the theory. Some of these universes may model ours well, while others may be unphysical. The typical problem in phenomenological string theory is determining which data give physical backgrounds. With the findings from this award, we now have a systematic way to study the backgrounds and try to answer this question. We now have a complete picture of the geometric properties of supersymmetric string backgrounds. This may lead us to understanding a topological phase of string theory which is more tractable from the full theory. We call these 'topological string theories' and versions of this have already been used to understand subsectors of string theory, and to study complex and symplectic geometry. There is a possibility that we can take that analysis further with the new geometric structures we have found. Finally, the links with geometric invariant theory mean that we may be able to find a notion of 'stability' for G2 structures and the Hull-Strominger system. These are two geometric structures that are of interest to mathematicians and physicists alike. |
| Sectors | Other |