Past Courses: 2012/2013 - School of Physical and Chemical Sciences

Title: Fun in Flatland: An Introduction to 3d QFTs

Three dimensional quantum field theories provide a nice testing grounds for exploring quantum field theory phenomena. Very simple UV theories can have highly nontrivial, and rich IR dynamics. These lectures will give a pedagogical review of various aspects of quantum field theory, including instantons, monopoles, the conformal window, vortices, skyrmions, Chern-Simons terms, etc., in the context of 3d quantum field theories. In the context of susy theories, we will review older work on exact results, mirror symmetry and duality, and also mention some more recent results.

Ken Intriligator

Schedule:
04/03/2013 16.00-18.00 Room LG1
05/03/2013 16.00-18.00 Room People's Palace 2
07/03/2013 16.00-18.00 Room 410
08/03/2013 16.00-18.00 Room LG1

Title: Instantons in Field Theory and String Theory

Massimo Bianchi ("Leverhulme Lectures")

These lectures are devoted to instantons in gauge theories and string theory and their role in generating non-perturbative effects. Special attention is devoted to the intriguing relation between instanton solutions in field theory and branes in string theory. In the first lecture, we discuss basic aspects of Yang-Mills instanton solutions and their bosonic and fermionic moduli. In the second lecture, we derive non-perturbative super potentials and other effects induced by instantons in supersymmetric gauge theories. We then pass to analyze instantons in string theory and discuss world-sheet instantons and brane-instantons. Finally we consider instantons in unoriented quiver theories that arise from D-branes at singularities.

References:

0) Coleman's Erice lectures 'Aspects of Symmetry' ('The uses of instantons')

1) Instantons and Supersymmetry. Massimo Bianchi, Stefano Kovacs, Giancarlo Rossi

2) Notes on unoriented D-brane instantons. Massimo Bianchi, Marine Samsonyan Int.J.Mod.Phys. A24 (2009) 5737-5763

3) Unoriented D-brane instantons. Massimo Bianchi, Gianluca Inverso Fortsch.Phys. 60 (2012) 822-834

Schedule:
16/01/2013 16.00-18.00 Room 208
30/01/2013 16.00-18.00 Room 208
06/02/2013 16.00-18.00 Room 208
19/02/2013 16.00-18.00 Room 208

Title: Graphs, Permutations and Strings

Sanjaye Ramgoolam

The perturbative computation of observables in quantum field theories ( QFTs) leads to sums of space-time (or momentum-space) integrals associated with Feynman graphs. QFTs with matrix degrees of freedom are of particular interest in gauge-string duality. The large N expansion of QFT correlators, where N is the matrix size, leads to a variation on Feynman graph counting, involving ribbon graphs or bipartite graphs embedded on surfaces. For both graphs and embedded graphs, the counting and enumeration can be expressed in terms of permutation groups. Lattice gauge theory, with permutation groups as gauge groups, and a simple (topological) choice of lattice action, plays a central role in exhibiting the geometry of these computations. This emergent geometry is related to (2D) string worldsheets and holomorphic maps. Covering maps involving 3D spaces also emerge from these counting problems. The geometric approach is closely connected to explicit counting formulae for infinite sequences of Feynman graphs or ribbon graphs.

Schedule:
14/11/2012 16.00-18.00 Room 208
21/11/2012 16.00-18.00 Room 208

Title: An Introduction to Generalised Geometry And M-Theory.

David Berman

In two lectures I will cover the M-theory version of "double field theory" which uses extended/generalised geometry to make the String theory U-duality groups a manifest symmetry.

Schedule:
17/10/2012 16.00-18.00 Room 208