There will be a summit meeting 21-22 March 2016 in the Mathematical Institute bringing together the Humboldt and Oxford mathematical physics groups with a focus on scattering amplitudes, correlation functions via integrability and twistor methods. Unlike many summit meetings, all are welcome.
Day 1 - 21th March 2016 (room L4, Andrew Wiles Building)
|9.30-10.30||Thomas Klose||Spectral Parameter Transformations of Holographic Wilson loops|
|11.00-12.00||Mathew Bullimore||Boundaries, Modules and Toda Systems|
|12.00-13.00||David Meidinger||Yangian-type symmetries of non-planar on-shell diagrams|
|15.00-16.00||Yvonne Geyer||Loop Integrands from the Riemann sphere|
|16.30-17.30||Tim Adamo||An AdS/CFT dictionary in twistor space|
Day 2 - 22nd March 2016 (room L5, Andrew Wiles Building)
|9.00-10.00||Matteo Rosso||Yangian invariance of N=4 super-Yang-Mills and ABJM|
One-Loop Soft Theorems via Dual Superconformal Symmetry
Six-point remainder function : an efficient approach in momentum space
Composite Operators and Form Factors in The Twistor Space
Formulation of N=4 SYM
|15.00-||Coffee and Tea|
List of Speakers:
Thomas Klose - "Spectral Parameter Transformations of Holographic Wilson loops"
Mathew Bullimore -" Boundaries, Modules, and Toda Systems"
Integrable systems are closely related to representation theory. A striking example is the N-body Toda chain, whose eigenfunctions are built from Whittaker vectors for the Lie algebra sl(N). I will explain how this construction appears in the study of three-dimensional gauge theories with N=4 supersymmetry in the presence of half-BPS boundary conditions.
David Meidinger -" Yangian-type symmetries of non-planar on-shell diagrams"
It is well known that planar on-shell diagrams, which correspond both to tree level amplitudes as well as leading singularities of planar amplitudes, are Yangian invariant. I will explain what remains of this symmetry for non-planar on-shell diagrams. Using the RTT realization of the Yangian it will be shown that these diagrams are still annihilated by Yangian generators which act on single boundaries of the diagram. The lowest levels of the symmetry are broken depending on the degree of nonplanarity. One can derive further identities involving integrable transfer matrices, in particular a conservation law for diagrams on cylinders.
Yvonne Geyer - "Loop Integrands 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 remarkably simple expressions on the Riemann sphere. My talk will focus on both supersymmetric and non-supersymmetric Yang-Mills theory and gravity, and discuss a proposal for the all-loop integrand.
Tim Adamo - "An AdS/CFT dictionary in twistor space"
Twistor theory has proven a useful language for the study of 4d CFTs, from both the kinematic (e.g., providing a set of variables on which the conformal group acts linearly) and dynamical (e.g., twistor actions for Yang-Mills theories) perspectives. The AdS/CFT correspondence tells us that in many cases of interest, strongly coupled 4d CFTs are dual to semi-classical (super)gravity in 5d AdS. I will argue that twistor theory is also a useful tool on the gravitational side of this duality. In particular, using a projective description of AdS_5 and its associated twistor space, some basic building blocks of AdS/CFT (bulk-to-boundary propagators, 2-point functions) can be described purely in terms of twistor data. I may also discuss the current limitations of this formalism and possibilities for overcoming them.
Matteo Rosso - "Yangian invariance of N=4 super-Yang-Mills and ABJM"
In this talk we derive the classical Yangian invariance of N=4 super-Yang-Mills and ABJM. We first define the meaning of "classical Yangian invariance" and describe the difficulties of understanding the Yangian as a symmetry of the action; we subsequently show that the equations of motion are invariant under the action of level-1 generators. We provide evidence of the consistency and nontriviality of the construction.
Edward Hughes - "One-Loop Soft Theorems via Dual Superconformal Symmetry"
Controlling infrared divergences in QFT cross-sections has been an important phenomenological problem for many decades. Recently, there has been renewed theoretical interest, with the observation that soft theorems emerge as the Ward identities of asymptotic symmetries, at least at tree level. I shall discuss recent work probing the one-loop corrections to subleading soft theorems in the context of N=4 super-Yang-Mills theory. In particular, I shall outline how hidden symmetries may be used to constrain the form of such corrections. Further, I shall present computations which determine the corrections precisely, revealing them to have a surprisingly simple form. These results may find fruitful application in QCD resummation and the development of holographic theories. This talk is based on the recent paper arXiv:1511.06716.
Johannes Broedel - "Six-point remainder function: an efficient approach in momentum space"
On the way towards a complete perturbative solution of (planar) N=4 sYM theory, the calculation of the remainder function takes a prominent role. While this is a considerable task in general kinematics, the situation is simpler in the multi-Regge regime: using a connection to the BFKL equation and solutions thereof, obtaining the momentum-space expression amounts to just performing a (rather cumbersome) Mellin-transform. After discussing the problem, describing the setup and describing the starting point, I will show, how to relate particular Mellin integrals. Using those relations, one can reduce the complete problem to the calculation of several master integrals, which in turn allows results up to very high loop orders.
Laura Koster/Matthias Wilhelm - "Composite Operators and Form Factors in the Twistor Space Formulation of N=4 SYM"
We incorporate composite operators in the twistor-space description of N=4 Super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganised into infinitely many interaction vertices and we argue that the same applies to composite operators. In the first half of this talk, we demonstrate these concepts using the concrete example of an operator consisting of two identical scalars. We propose its expression in twistor space and probe this by computing its tree-level MHV form factors. In the second half, we argue that this formalism can be extended to all gauge-invariant local composite operators of the theory. We construct their vertices from Wilson loops and find that they immediately generate all tree-level MHV form factors for all operators.
List of participants:
University of Oxford
|Rest of the World
Further details will appear on this page.