There will be a summit meeting 2122 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.
Schedule
Day 1  21th March 2016 (room L4, Andrew Wiles Building)
Time  Speaker  Title  

9.009.30  Registration  
9.3010.30  Thomas Klose  Spectral Parameter Transformations of Holographic Wilson loops  
10.3011.00  Coffee break  
11.0012.00  Mathew Bullimore  Boundaries, Modules and Toda Systems  
12.0013.00  David Meidinger  Yangiantype symmetries of nonplanar onshell diagrams  
13.0015.00  Lunch break  
15.0016.00  Yvonne Geyer  Loop Integrands from the Riemann sphere  
16.0016.30  Coffee break  
16.3017.30  Tim Adamo  An AdS/CFT dictionary in twistor space  
19.00  Dinner 
Day 2  22nd March 2016 (room L5, Andrew Wiles Building)
Time  Speaker  Title  

9.0010.00  Matteo Rosso  Yangian invariance of N=4 superYangMills and ABJM  
10.0010.30  Coffee break  
10.3011.30 
Edward Hughes 
OneLoop Soft Theorems via Dual Superconformal Symmetry 

11.3012.30 
Johannes Broedel 
Sixpoint remainder function : an efficient approach in momentum space 

12.3014.00  Lunch break  
14.0015.00 
Laura Koster Matthias Wilhelm 
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 Nbody 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 threedimensional gauge theories with N=4 supersymmetry in the presence of halfBPS boundary conditions.
David Meidinger " Yangiantype symmetries of nonplanar onshell diagrams"
It is well known that planar onshell 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 nonplanar onshell 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 highergenus worldsheets required to describe loop effects. I will describe how in such worldsheet models based on the scattering equations, formulae on highergenus surfaces can be transformed to remarkably simple expressions on the Riemann sphere. My talk will focus on both supersymmetric and nonsupersymmetric YangMills theory and gravity, and discuss a proposal for the allloop 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 YangMills theories) perspectives. The AdS/CFT correspondence tells us that in many cases of interest, strongly coupled 4d CFTs are dual to semiclassical (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 (bulktoboundary propagators, 2point 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 superYangMills and ABJM"
In this talk we derive the classical Yangian invariance of N=4 superYangMills 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 level1 generators. We provide evidence of the consistency and nontriviality of the construction.
Edward Hughes  "OneLoop Soft Theorems via Dual Superconformal Symmetry"
Controlling infrared divergences in QFT crosssections 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 oneloop corrections to subleading soft theorems in the context of N=4 superYangMills 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  "Sixpoint 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 multiRegge regime: using a connection to the BFKL equation and solutions thereof, obtaining the momentumspace expression amounts to just performing a (rather cumbersome) Mellintransform. 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 twistorspace description of N=4 Super YangMills 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 treelevel MHV form factors. In the second half, we argue that this formalism can be extended to all gaugeinvariant local composite operators of the theory. We construct their vertices from Wilson loops and find that they immediately generate all treelevel MHV form factors for all operators.
List of participants:
Humboldt University

University of Oxford

Rest of the World

Further details will appear on this page.