Hi!
This is the personal home page of Gerard Watts. member of the theoretical physics group in the Mathematics Department of King's College London

I've put on here some of my old lecture notes, some of my old papers which are hard to find and some notes on my current research projects.

Research

At the moment I am researching into three areas, all within the general area of two dimensional field theory, usually quantum, often conformally invariant. Here are three specific topics as examples.

Firstly: defects.

These are discontinuities in the surface on which a field theory is defined. In integrable quantum field theory they have nice, or not-so-nice, algebraic definitions. One of the nice properties they have is a "reflection coefficient", first defined by Ingo Runkel, Thomas Quella and me in 2006. This has recently been given a more physical basis by Marco Meineri, Joao Penedones, Antonin Rousset in arxiv.org/1904.10974. Most recently, I worked on calculating it in perturbation theory with mny recent graduate student, Isao Makabe, in arxiv.org/1712.07234. I am also interested in boundaries, in the space of boundaries and defects and how they are connected by renormalisation group flows and am also working actively on these. This has also led to new results for fermionic conformal field theories with my old student Ingo Runkel, in arXiv:2001.05055 where we showed that the assignment of bosonic or fermionic is up to you, for some theories.

Secondly: W-algebras.
These are interesting algebraic objects invented by Zamolodchikov in 1985 and subsequently generalised to the extent that they are ubiquitous in conformal field theory and their definition is almost content-free. However, the original models defined are still special enough that there has been work on them continuously since their invention. Most recently I worked with another of my PhD students, Nick Iles, on the traces over W-algebra generators and their modular properties. We wrote two (nice) papers and have the usual collection of as-yet unpublished results which may surface some time.

Finally: thermal theories and generalisations

I worked in a very interesting collaboration with Benjamin Doyon, Alvise Bastianello and Takato Yoshimura on generalised hydrodynamics in a classical field theory in both thermal and generalised Gibbs ensembles. I find generalised Gibbs ensmbles (GGEs) fascinating and investigating some of their properties in the quantum case

Here is an animation of some of the numerical work in arxiv.org/1712.05687 on the time-evolution of energy and momentum densities in a classical field theory with different parts starting at two different temperatures:

Old papers

Lecture on Conformal Blocks

This is here, together with extra material

Old lecture notes

I am afraid that these are not all yet ready - my old lecture notes on "Low dimensional quantum field theory" will be typed up at some stage.

Lecture notes on Spacetime Geometry and General Relativity (2016)

Lecture notes on Low Dimensional Quantum Field Theory (2013)