Details of Grant 

EPSRC Reference:	EP/F043791/1
Title:	Wilson Loops in Gauge and String Theories
Principal Investigator:	Ricci, Dr R
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Physics
Organisation:	Imperial College London
Scheme:	Postdoc Research Fellowship
Starts:	01 October 2008	Ends:	30 September 2011	Value (£):	238,432
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
With the exception of gravity all the fundamental interactions present in Nature have been given a common mathematical foundation based on a symmetry principle known as gauge symmetry. For this reason these theories are called gauge theories. The paradigmatic and best understood example is electromagnetism, the theory which describes the interactions of photons with matter. Another important example is quantum chromodynamics which describes the interactions of gluons, the carriers of the interaction, and quarks inside atomic nuclei. Both gluons and quarks have a charge known as colour which can be thought as a generalization of the ordinary electric charge of electromagnetism. Experimental evidence reveals that quarks and gluons cannot be directly observed due to a fundamental property known as colour confinement . Only particles such as protons and neutrons that contain quarks and gluons, but have no net color themselves, can be directly observed. The main reason for colour confinement is that the interaction is strong : If we try to pull apart a quark from, say, an antiquark, which has same mass and spin but opposite colour, the force increases linearly with the distance therefore preventing their separation. At a more formal level we say that the gauge coupling, which roughly measures the strength of the interaction, is strong and that the theory is strongly coupled. The physical picture is then very different from what happens in electromagnetism where the coupling is small and requires the introduction of fundamental new ideas in both physics and mathematics. This explains why a rigorous proof of colour confinement is a long sought goal not only of theoretical physicists but also of mathematicians, its achievement being worthy of a Clay Institute Millennium Prize! A key quantity in the study of strongly coupled theories and colour confinement is the Wilson loop named after the physicist Kenneth Wilson. Imagine the propagation of quark-antiquark pair along a closed trajectory (loop) in spacetime. The probability for such a process to happen depends on the shape of the trajectory and it is measured by the Wilson loop. This quantity is very important as from it we can extract the force which binds together the quark and antiquark and which is ultimately responsible for confinement. A rigorous proof of confinement via the study of Wilson loops is one of the most outstanding challenges of mathematical physics.In recent years a dramatic improvement in our understanding of gauge theories has come from an a-priori unexpected direction that is from the study of string theory, the most promising candidate for unifying Einstein's theory of gravity with other interactions. The basic assumption of string theory is that the ultimate building blocks of nature are extended, string-like, objects: As a string of a violin produces different sounds depending on how it is plucked, the different excitations of these elementary strings correspond to different elementary particles. Some string theories are conjectured to be equivalent (dual) to gauge theories in the sense that all the basic phenomena of the latter can be in principle described and understood by using the language of string theory. This complementary point of view has turned out to be very fruitful since it can help to attack and eventually solve problems which would be otherwise out of reach. Furthermore it has been very beneficial to our understanding of Wilson loops which, in string theory, receives a beautiful geometrical reinterpretation as surfaces with boundaries. This dual description opens the way to a new understanding of gauge theory dynamics and gives us the analytical tools to study colour confinement. The study of Wilson loops and the exploration of their many connections with Mathematical Physics is the focus of my research. The hope is that it will lead to genuinely new insights into the study of both gauge and string theories.
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Organisation Website:	http://www.imperial.ac.uk