North British Mathematical Physics Seminar 26

The twenty-sixth meeting of the North British Mathematical Physics Seminar will take place on Tuesday 29th June 2010 at the University of York. Coffee/tea will be in G/109 in the Department of Mathematics, on the first floor of James College, with talks in G/002 downstairs.


José Figueroa-O'Farrill (Edinburgh)
Supersymmetric M2-branes and A-D-E
Eleven-dimensional supergravity admits solutions describing electric membranes. In particular, those which preserve some supersymmetry play an important rôle in the gauge/gravity correspondence. In this talk I will describe a partial classification of supersymmetric membrane solutions and will make contact with the McKay correspondence between finite subgroups of the quaternions and simply-laced Dynkin diagrams.
Atsushi Higuchi (York)
Interacting quantum fields in de Sitter space
In interacting field theory in de Sitter space the free-theory vacuum state appears to decay by spontaneous emission of particles in perturbation theory. This observation led Polyakov to argue that de Sitter space is unstable and that the cosmological constant is screened as a result. On the other hand, Marolf and Morrison have shown recently that the vacuum state in the Euclidean approach for scalar field theory does not show any sign of instability. We argue in this work that the Euclidean vacuum state and the cosmological in-in vacuum state, which exhibits apparent particle emission, are in fact equivalent, and discuss how this vacuum state can be stable and de Sitter invariant in spite of the apparent spontaneous particle emission.
Anatoly Konechny (Heriot-Watt)
Gradient formula for the beta-function of 2D quantum field theory
I will discuss a gradient formula for beta functions of two-dimensional quantum field theories. The gradient formula has the form ∂i c = - (gij+Δgij+bij) βj, where βj are the beta functions, c and gij are the Zamolodchikov c-function and metric, bij is an antisymmetric tensor introduced by H. Osborn and Δgij is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behaviour the most significant of which is the condition that the large distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to non-linear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c. The talk is based on a joint work with Dan Friedan.
Dan Brattan (Durham)
Charged, conformal non-relativistic hydrodynamics
We embed a holographic model of an U(1) charged fluid with Galilean invariance in string theory and calculate its specific heat capacity and Prandtl number. Such theories are generated by a R-symmetry twist along a null direction of a N=1 superconformal theory. We study the hydrodynamic properties of such systems employing ideas from the fluid-gravity correspondence.
Giorgos Papageorgiou (Heriot-Watt)
Galilean quantum gravity in 2+1 dimensions
I will discuss classical and quantum gravity in 2+1 dimensions in the Galilean limit. Although there are no Newtonian forces between massive objects in (2+1)-dimensional gravity, the Galilean limit is non-trivial and topological interactions are still present. In order to capture these topological aspects, I consider the Chern-Simons theory of a two-fold central extension of the Galilei group and, similarly, the so-called Newton-Hooke group. I show that the Lie algebras of these two groups admit a nondegenerate, invariant bilinear form. Using this form, I define Galilean gravity (with or without a cosmological constant) as the Chern-Simons theory of the relevant centrally extended group. I then show how to quantise the said Chern-Simons theory using a Hamiltonian approach. Many aspects of the quantum theory are determined by two quantum groups: the quantum double of the extended homogeneous Galilei group (in the absence of a cosmological constant), and the quantum double of a certain q-deformation of that same group (when a cosmological constant is present).

Practical Information

Maps of York showing the location of the university campus can be obtained here and here. Mathematics is in James College (see the campus map. Note that we're in the same building as before, which used to be known as Goodricke College. But the new Goodricke College is 1km away, on the new east campus). Here is the list of car parks on campus. The taxi fare from the railway station is around £7. Buses (no.4) are every 10 minutes: fare £1.80. The station is on the north-west side of York while the campus is about a mile and a half south-east of the city centre: the walk takes about 35 minutes.

National Rail Enquiries

Drinks and biscuits will be provided free of charge.

We'll have lunch on campus (paying individually), at Wentworth College.

Limited funds are available to help with travel expenses of those with no other source of funding, especially postgraduate students and postdocs. Please book early to take advantage of the cheaper advance-purchase train fares.

If you wish to attend the meeting, or for further questions, please email the local organiser Niall MacKay.

Financial Matters

Participants are asked to complete the banking details form (if you have not done so in the past) and the expense claim form (project section), print and sign and post to Miss Lisa Keyse, Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS.


These people participated in the meeting.

José Figueroa-O'Farrill
Last modified: 16 Jun 2010 at 14:09 BST