Details of Grant 

EPSRC Reference:	EP/F043635/1
Title:	Geometric Phases in String Theory
Principal Investigator:	Sonner, Dr J
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Physics
Organisation:	Imperial College London
Scheme:	Postdoc Research Fellowship
Starts:	01 December 2008	Ends:	30 November 2011	Value (£):	236,737
EPSRC Research Topic Classifications:	Mathematical Physics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 13 Mar 2008 Mathematics Postdoctoral Interview Panel Announced 14 Feb 2008 Maths Postdoctoral Fellowships 2008 InvitedForInterview
Summary on Grant Application Form
String Theory aims to unify quantum mechanics with the general theory of relativity. The former applies to the world of atoms, molecules and elementary particles, whereas the latter applies to physics processes at the scale of our solar system, of galaxies and the Universe as a whole. While both theories work extremely well in their respective regions of validity, they are mutually incompatible in realms where they both apply. String Theory avoids this incompatibility by starting from the hypothesis that the fundamental objects defining the correct unified theory are one-dimensional strings rather than zero-dimensional point particles. In fact, modern versions of string theory don't stop there. Rather they contain fundamental building blocks of still higher dimension. These objects are termed D-branes as a generalisation of the word membrane for two-dimensional objects. These branes (and strings) are the fundamental building blocks of space and time and their bound states are the molecules making up its fabric.My quantity of interest in this proposal is the so-called Berry phase or Berry holonomy of a system of D-branes. The Berry holonomy is a subtle quantum mechanical effect that was first described in detail by Berry in the 1980ies, but has made several un-noticed appearances in the physics of atoms and molecules already in the early days of quantum physics. The canonical example of a system containing a Berry phase is in fact that of a molecule in which the heavy nuclei correspond to the slow degrees of freedom and the electrons to the fast degrees of freedom. The separation between slow and fast degrees of freedom allows us to apply a number of simplifying methods, subsumed in the so-called 'adiabatic approximation'. In such cases, the dynamics of the fast objects spontaneously create a gauge connection, that is a generalised magnetic field, which we may interpret as giving rise to the Berry phase. The resulting (generalised) magnetic fields affect the motion of the slow constituents.In my research I propose to study the quantum structure of D-brane molecules, i.e. bound states of branes with special regard to the effect just described. It should come as no surprise that some of the tools used in this study are contemporary updates of the very same methods used by the pioneers of quantum mechanics in their quest to explain chemistry and the quantum properties of matter from first principles. For instance, the application of the Born-Oppenheimer method (first described by Born and Oppenheimer in 1927) to D-brane bound states allows us to identify the analogs of electrons as fundamental strings stretching from one brane to another and the analogues of heavy nuclei as the branes these strings end on.The project proposed here will result in a deeper understanding of such bound states, but in generalising methods from atomic and condensed matter physics to string theory we will also be able to give something back in return: String Theory has a rich geometrical structure that allows us to develop new powerful mathematical techniques that can then again be exported to condensed matter physics and other disciplines. This will allow us to solve certain (strong-coupling) problems applicable to condensed matter physics that have hitherto eluded solution by conventional techniques. In this way it is hoped that certain mathematical aspects of String Theory will lead to testable predictions in the field of condensed matter physics. The project proposed here will also further interactions among researchers in these fields with string string theorists leading potentially to a powerful inter-disciplinary alliance with benefits for either side.
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Organisation Website:	http://www.imperial.ac.uk