Download THEO-Waldram-2

MSci Project Proposal Form 2010-2011
Project Code: THEO-Waldram-2
Project title: Supergravity and generalized geometry
Supervisor: Prof. Daniel Waldram
Assessor: Prof. Kelly Stelle
Telephone: Ex. 4 7645
Telephone: Ex. 4 7826
E-mail: d.waldram
E-mail: k.stelle
Research Group: Theoretical physics
Research Group: Theoretical Physics
Project Summary:
String theory is a putative quantum theory of gravity which in addition proposes to unify the known
forces and particles of the standard model. The central idea is that the fundamental objects are not
point particles but tiny vibrating loops or strings. The size of the strings is typically set by the Planck
scale (10-33 cm) so at all measurable scales they appear as point particles. There has recently been a
remarkable conjecture that what were previously regarded as five different versions of string theory
are all actually related by subtle symmetries known as “dualities”.
The goal of the project is to provide a basic introduction to “generalized geometry”. This is an
extension of conventional Riemmanian geometry that is useful for describing the generalizations to
General Relativity that arise in the low-energy approximation of string theory. Since string theory is a
theory of gravity, it’s low-energy classical description must be General Relativity. In fact one finds an
version of Einstein’s theory with a particular matter content, known as “supergravity”. This has an
additional symmetry, which relates fermions and bosons. In the project, we will focus on some simple
forms of supergravity, trying to understand the matter content and the form of the equations of
motion. We will then introduce the notion of “generalized geometry” that provides a description of
both the metric and the new matter in a unified way. Understanding the structure of generalized
geometry is a topic of current research interest.
This is a purely theoretical project and requires a strong theoretical and mathematical background.
The calculations are all classical, but you will need a very good understanding of geometry and
general relativity as well as group theory. The objective is very much to do the detailed calculations
required to understand the properties of the theory rather than give broad-brush descriptions.
Interested students should contact the supervisor for more information.
Experimental component:
0%
Computational component: 0 %
Theoretical component:
100 %
Is the MSci Project eligible for students on the MSci
Physics with Theoretical Physics Degree: YES
Are workshop facilities required: NO
Suggested reading (at least one relevant reference):
Barton Zwiebach, “A First Course in String Theory”, CUP
Joseph Polchinski, “String Theory, Vol. 1”, CUP
John H. Schwarz, “Status of Superstring and M-Theory”, http://arxiv.org/abs/0812.1372
Edward Witten, “Reflections on the Fate of Spacetime”,
http://www.sns.ias.edu/~witten/papers/Reflections.pdf
Imperial College of Science, Technology, and Medicine