The c/a theorem and QFT in curved spacetime

Graham Shore, Swansea University
30.09.2013 to 04.10.2013


The c/a theorem is a fundamental result in quantum field theory constraining
the nature of renormalization group flows and the relation of UV and IR physics.
In the first part of these lectures, we will review early attempts to generalise the
2-dim Zamolodchikov c-theorem to four dimensions, then discuss the 2011 proof
of a 4-dim a-theorem by Komargodski and Schwimmer together with recent
developments and speculations. In the second part, we will discuss QFT in curved
spacetime and show how the background geometry induces a novel analytic
structure for Green functions with important consequences for causality, unitarity,
dispersion relations and the optical theorem, all of which play a vital role in proving
the c/a theorem in flat spacetime.
You can read a nice summary of the current debate on the a-theorem here:

Approximately 6 hours lectures (tba)

Bound states in gauge theory

Paul Hoyer, University of Helsinki
30.09.2013 to 04.10.2013

The aim of understanding hadrons as bound states of QCD motivates a  study of how
atoms emerge in QED perturbation theory. The properties  of atoms in motion illuminate
relativistic effects on bound states, such as Lorentz contraction in quantum physics. The
Dirac equation results from summing a certain subset of Feynman diagrams. The Dirac  
spectrum reflects the degrees of freedom of a single electron even though the Fock
states  have any number of electron-positron pairs. The solutions of the Dirac equation
for a confining (linear) potential are qualitatively different from those obtained with a 1/r
potential. The  QED  experience suggests an approach to hadrons which is consistent
with the field theory rules of QCD.

Approx 6 hours lecture (tba)

Higher spin theories

Dario Francia, Scuola Normale Superiore Pisa
30.09.2013 to 04.10.2013

In these lecture we shall provide an introduction to the basics of higher-spin theory.
We shall start with the general structure of the free theory (metric-like and frame-like
approaches in flat and (A)dS bkg, for symmetric and mixed-symmetry fields) to then
move to illustrate the main difficulties met at the interaction level. In the second part
of the course we shall deal with positive results about higher-spin non-linear theories,
including the construction of cubic vertices and Vasiliev's equations. The idea is to
provide an introduction to the essential language and techniques used in the literature,
to highlight some technical steps in a concrete way and to indicate a few open directions.

Approx 6 hours lecture (tba)


Introduction to Gauge Theory

José Figueroa O'Farrill (University of Edinburgh), Bernd Schroers (Heriot Watt), Brendan Owens (Glasgow University) and Christian Sämann (Heriot Watt)
09.09.2013 to 18.09.2013

An advanced course titled 'Introduction to Gauge Theory' will be given by José Figueroa O'Farrill, Bernd Schroers, Brendan Owens and Christian Sämann as part of the Scottish Mathematical Sciences Training Centre (SMSTC) this September. The course will cover the geometry of gauge theory and applications of gauge theory in physics. It is aimed at PhD students in SMSTC departments, but anybody interested is welcome to attend.

Contents and Purpose

Gauge theory plays a fundamental role in modern physics. It is the language in which the standard model of elementary particle physics is formulated. At the same time it has had deep and surprising applications to geometry and topology in four dimensions (Donaldson and Seiberg-Witten theory) and three dimensions (Chern-Simons theory, Floer homology). The purpose of the course is to introduce the basic mathematical concepts and ideas of gauge theory. The course builds to some extent on the existing SMSTC course Geometry and Topology and assumes a basic understanding of manifolds and differential forms. However, necessary tools from Lie groups will be introduced in the first lectures. The course will outline some of the applications of gauge theory in particle physics but will not include a systematic treatment of quantisation.



The course will be delivered by a team of lecturers from the Uinversity of Edinburgh, the University of Glasgow and Heriot-Watt University. The lectures can be attended via the SMSTC video facilities at Glasgow (room 104 in the Maths Department) Edinburgh (room 5325 in JCMB) and Heriot-Watt (room T01 in the Colin Maclaurin Building).

All lectures will take place 2-4pm at the dates given below. The material for the lectures will be uploaded as the course progresses.


Monday, 9 Sept 2-4pm, José Figueroa O'Farrill, Introduction to Lie Algebras and Lie Groups  

Wednesday, 11 Sept 2-4pm, Bernd Schroers, Introduction to Gauge Theory

Friday, 13 Sept 2-4pm, Brendan Owens, Fibre Bundles and Connections

Monday, 16 Sept 2-4pm Bernd Schroers and Christian Sämann, Monpoles and Instantons

Wednesday, 18 Sept 2-4pm, Christian Sämann, ADHM Construction and Instanton Moduli Spaces