5th South East Mathematical Physics Seminars

The 5th meeting of the South East Mathematical Physics Seminars will be held on Friday 6 November 2015 at the University of Surrey in 39/40AA04, LTM and 24AA04.

There is no registration fee, but it would be helpful if you could please register here.

Timetable

10:00 - 11:00 Coffee in 39/40AA04; The venue for the morning session is LTM.; 11:00 - 11:50 Nicholas Manton (DAMTP, Cambridge) Hyperbolic Vortices; 11:50 - 12:40 Fedor Levkovich-Maslyuk (King's College, London) Numerical Solution of the Spectral Problem and BFKL at Next-to-Next-to-Leading Order in N=4 SYM; 12:40 - 14:00 Lunch; The venue for the afternoon session is 24AA04.; 14:00 - 14:50 Yvonne Geyer (Oxford) Loop Integrands for Scattering Amplitudes from the Riemann sphere; 14:50 - 15:40 Benoit Vicedo (Hertfordshire) From Classical R-matrices to Deformed Integrable Sigma Models; 15:40 - 16:10 Tea & Coffee in 39/40AA04; 16:10 - 17:00 Giulia Ferlito (Imperial College, London) Coulomb Branch and Moduli Space of Instantons; Nicholas Manton (DAMTP, University of Cambridge); Hyperbolic Vortices; Abelian Higgs vortices on the hyperbolic plane are integrable, and explicitly known. Vortices on compact hyperbolic surfaces are trickier to construct but some especially symmetric examples have now been found (work with Rafael Maldonado). The vortices have a clear, purely geometrical interpretation.; Seminar 1 by Nicholas Manton; Fedor Levkovich-Maslyuk (King's College, University of London); Numerical Solution of the Spectral Problem and BFKL at Next-to-Next-to-Leading Order in N=4 SYM; I will present a simple numerical method for computing the spectrum of anomalous dimensions in planar N=4 super Yang-Mills at finite coupling. It is based on the Quantum Spectral Curve originating from integrability of the theory. The method allows us for the first time to obtain the exact spectrum of a non-trivial interacting QFT in 4d with almost unlimited precision. I will show examples with 80 digits accuracy and also explore numerically the rich cut structure for twist operators with complexified spin. Inspired by these numerical results, a new analytic method will be presented which gives a systematic weak coupling expansion for any operator. In particular it leads to a new analytic result for the BFKL (Balitsky-Fadin-Kuraev-Lipatov) eigenvalue at next-to-next-to-leading order.; Seminar 2 by Fedor Levkovich-Maslyuk; Yvonne Geyer (University of Oxford); Loop Integrands for Scattering Amplitudes from the Riemann sphere; Worldsheet formulations of quantum field theories have had wide ranging impact on the study of scattering amplitudes. However, the mathematical framework becomes very challenging on the higher-genus worldsheets required to describe loop effects. I will describe how, in such worldsheet models based on the scattering equations, formulae on higher-genus surfaces can be transformed to ones on the Riemann sphere. My talk will focus on the remarkably simple new formulae emerging for super-Yang-Mills and gravity, and discuss the proposal for the all-loop integrands.; Seminar 3 by Yvonne Geyer; Benoit Vicedo (University of Hertfordshire); From Classical R-matrices to Deformed Integrable Sigma Models; I will present a general framework for constructing integrable deformations of integrable sigma models within the Hamiltonian formalism. It can be applied to a large class of non-ultralocal models, including the AdS₅ x S⁵ superstring, and can be used to describe both 'Yang-Baxter' type and 'gauged WZW' type deformations which are currently the subject of intensive study. The construction also makes it apparent why these two types of integrable deformations are related by Poisson-Lie T-duality.; Giulia Ferlito (Imperial College, University of London); Coulomb Branch and Moduli Space of Instantons; Moduli spaces of instantons are a very rich laboratory where physicists and mathematicians enjoy a fruitful interaction. Some of the most exciting corners of this lab are unveiled using supersymmetric gauge theories. It has long been known, for example, that the Higgs branch of certain quiver gauge theories with 8 supersymmetries is isomorphic to the moduli space of G-instantons of charge k, where G is any of the classical groups.; In this talk I exploit another avenue, namely that the moduli space of k G instantons is isomorphic to the Coulomb branch of some particular quiver gauge theories in 3d. I will show how we have learnt to calculate a partition function that counts gauge invariant operators on the chiral ring of the Coulomb branch, making use of some special objects called monopole operators. The construction of this partition function allows us to study the moduli space of instantons for any group G, including non-simply laced exceptionals.; Seminar 5 by Giulia Ferlito
The meeting is partially supported by a London Mathematical Society Joint Research Groups grant. 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 Clare Dunning (tcd@kent.ac.uk) in advance if you would like to apply for support. Participants
List of Registered Participants: Andrea Prinsloo (Surrey); Alessandro Torrielli (Surrey); Clare Dunning (Kent); Nicholas Manton (DAMTP); Fedor Levkovich-Maslyuk (King's); Yvonne Geyer (Oxford); Benoit Vicedo (Hertfordshire); Giulia Ferlito (Imperial); Aindriu Conroy (Lancaster); Andrea Fontanella (Surrey); Charles Young (Hertfordshire); Antonio Pittelli (Surrey); Martyna Kostacinska (Queen Mary); Jock McOrist (Surrey); Joakim Strömvall (Surrey); Spyridon Talaganis (Lancaster); Riccardo Borsato (Imperial); Jan Gutowski (Surrey); Vincent Caudrelier (City); Thomas Winyard (Durham); Martin Wolf (Surrey); Steffen Krusch (Kent); Nicholas Iles (King's); Gerard Watts (King's); Paul Dempster (Surrey); Sara Pasquetti (Surrey); Amihay Hanany (Imperial)

5th South East Mathematical Physics Seminars

Timetable

Seminar Programme

Practical Information

Participants