40th North British Mathematical Physics Seminar

The 40th meeting of the North British Mathematical Physics Seminar will be held on Wednesday 26 March 2014 in Daniel Rutherford building, lecture theatre 2 at the King's Buildings UoE campus. For all general information about the North British Mathematical Physics Seminar, including instruction for claiming travel expenses follow this link


Coffee/Tea at Daniel Rutherford building
Anastasia Doikou (Heriot-Watt University)
Algebraic description of classical and quantum integrable defects
A systematic approach to classical integrable defects is proposed, based on an underlying Poisson algebraic structure. Local integrals of motions are constructed as well as the time components of the corresponding Lax pairs for the sine-Gordon model. Continuity conditions imposed upon the time components of the Lax pair to all orders give rise to sewing conditions, which turn out to be compatible with the hierarchy of charges in involution. At the quantum level, using the Bethe ansatz methodology, we extract the transmission amplitudes for the XXZ model. These describe the interaction between the particle-like excitations displayed by the model and the spin impurity. In the attractive regime of the XXZ model, we also derive the breather's transmission amplitude.
Lunch Some suggestions
Daniel Waldram (Imperial College, London)
Consistent truncations and generalised geometry
The study of consistent truncations of gravitational theories is an old subject going back to work of Jordan and Pauli. It is well known that reductions on group manifolds are consistent, but there is also a mysterious set of truncations on very particular coset manifolds with non-trivial form- field fluxes. We show how generalised geometry gives a unified description of such reductions. In particular we demonstrate that all round-sphere S^d geometries admit "generalised parallelisations´┐Ż, giving a simple way to understand the remarkable consistent truncations on S7, S5 and S4.
Tim Goddard (Durham)
Calculating Multi-Loop Scattering Amplitudes in N=4 SYM
N=4 SYM is a highly symmetric QFT which in recent years has been shown to have dualities to Wilson Loops and Correlation Functions, which imply other hidden symmetries. I will talk on work done with collaborators in arXiv:1312.1163, where we use the Amplitude/Correlator duality to calculate the amplitude integrand up to 5-loops, and in the parity-even sector up to 6-loops. This work was primarily discussed through the language of simple graph theory and it is this language and approach which, I hope to demonstrate, avoids the calculational problems of classic Feynman diagrams.
Tea at Daniel Rutherford building
Rouven Frassek (Durham)
Bethe Ansatz for Yangian Invariants: Towards scattering amplitudes
Tree-level scattering amplitudes in N=4 super Yang-Mills theory are Yangian invariant. This symmetry suggests that there is an underlying integrable structure. Inspired by Baxter's Perimeter Bethe Ansatz we present a method to construct Yangian invariants. The condition for Yangian invariance is formulated as an eigenvalue problem of certain monodromies that can be solved using Bethe Ansatz techniques. The rather general principle is being worked out for rational inhomogeneous spin chains. Using the Algebraic Bethe Ansatz we derive Bethe equations for Yangian invariants and study the corresponding on-shell Bethe vectors. Furthermore, we show how they can be reformulated in terms of contour integrals. This aspect is reminiscent of an on-shell formulation of scattering amplitudes in N=4 super Yang-Mills theory.
Carmen Li (University of Edinburgh)
Three-dimensional black holes and descendants
We determine the most general three-dimensional vacuum spacetime with a negative cosmological constant containing a non-singular Killing horizon. We show that the general solution with a spatially compact horizon possesses a second commuting Killing field and deduce that it must be related to the BTZ black hole (or its near-horizon geometry) by a diffeomorphism. We show there is a general class of asymptotically AdS3 extreme black holes with arbitrary charges with respect to one of the asymptotic-symmetry Virasoro algebras and vanishing charges with respect to the other. We interpret these as descendants of the extreme BTZ black hole.

Practical Information

You can get to King's buildings from the Waverly station by bus in about 20min. It takes 5-10 min to walk from the bus stop to Daniel Rutherford building. Here is a link to a handy bus guide for King's buildings here .

Here is a link to UoE campus maps campus maps .

Train information can be obtained from here.

Limited funds are available to help with travel expenses of participants with no other source of funding. We hope that this will encourage postgraduate students and postdocs to attend the meeting. Please email Douglas Smith in advance if you would like to apply for support.

Postscript: The meeting took place successfully. Click here to view a list of people who took part.

Anatoly Konechny
Last modified: Fri Mar 21 18:12:19 CET 2014