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From one to arbitrary loops in six dimensions (20' + 10')30m
Some of the most recent cutting edge results for two-loop five gluon/parton amplitudes have been obtained using dimensional regularisation in an integer number of dimensions, namely D=6. Starting from such six-dimensional calculations it is possible to obtain results in a generic D=4-2ε dimension: this technique is known as dimensional reconstruction. In this talk I will briefly retrace the origin of the method discussing first one loop applications and then outlining the two-loop case. I will then focus on the viability of higher loop generalisations of the method and its application to form factors, showing that in principle D=6 is enough to obtain complete results at arbitrary loop order.
Manuel Accettulli Huber
Dual conformal box integral in Minkowski space (20' + 10')30m
The dual conformal box integral is the simplest of a series of 'fishnet' Feynman integrals describing the correlation functions of a strongly twisted version of N=4 super Yang-Mills. In Euclidean space this integral has been shown to possess an extra copy of conformal symmetry in region momenta space, known as "dual" conformal symmetry. The situation is more subtle in Minkowski signature, and the Euclidean results may not carry over as easily as previously thought. In this talk I will discuss recent attempts to understand the extent to which dual conformal symmetry of the box integral is preserved in Minkowski signature. One issue is the fact that conformal group does not act transitively on Minkowski space, so I will describe the U(2) compactification, which adds a twisted light cone at infinity. This compactification allows for visualisation of how the conformal group acts on Minkowski space, even on points at infinity.
(Humboldt University Berlin)
From scattering amplitudes to observables in post-Minkowskian gravity (20' + 10')30m
In General Relativity the post-Minkowskian scattering angle between relativistic particles is an important observable since it could lead to improved gravitational wave templates (arXiv:1609.00354). In this regard, using a relativistic Lippman-Schwinger equation, we will present a novel relation where this observable can be computed directly from the classical part of a scattering amplitude. We will see how this relation express the scattering angle purely in terms of on-shell amplitudes and to any order in the gravitational coupling, avoiding to introduce a potential at any intermediate step of the calculation as done with previous methods.
To conclude, we will present a remarkable connection with other on-shell formalisms as the eikonal limit.
(Neils Bohr Institute)
On higher-derivative effects on the gravitational potential (20' + 10')30m
Much work has been devoted recently to studying the effects of possible modifications of Einstein-Hilbert (EH) gravity. Apart from adding a cosmological constant, the conceptually simplest modifications consist in adding terms with higher powers of the curvature to the EH action. Quadratic and cubic corrections make an appearance in the effective gravitational action for closed strings, and as counterterms at one loop in gravity coupled to matter and at two loops in pure gravity. In particular, we want to see whether and how higher-derivative corrections affect the Newtonian potential.
Stefano De Angelis
MHV, anti-MHV amplitudes and the squared Amplituhedron (20' + 10')30m
The on-shell superspace formulation of N=4 SYM allows the writing of all possible scattering processes in one compact object called the super-amplitude. Famously, the super-amplitude integrand can be extracted from generalized polyhedra called the amplituhedron. In the paper arXiv:1701.00452v3 a new geometrical object is introduced called the correlahedron, conjectured to be equivalent to stress-energy correlators. These are intimately related to planar amplitudes, giving them in multiple lightlike limits. In this talk I will review some geometrical aspects of the amplituhedron, also giving a graphical visualization, and show some recent results on its connection with a lightlike limit of the correlahedron
Introduction to the Sigma package (20' + 10')30m
When computing scattering amplitudes in quantum field theories such as quantum chromodynamics, the structure of the integrals and the sums involved is becoming very quickly quite complicated, and we need more powerful tools in order to compute them more efficiently. In this talk, we will present the summation package Sigma of RISC by Carsten Schneider, which allows to simplify nested sum calculations by either computing their closed form directly or by reducing their nested depth and trying to express them in a « simpler » form. We will present the underlying principles — in particular the telescoping paradigm, its extensions and the solving of linear recurrence equations — and supplement them with different examples of applications, before moving to difference ring theory, the actual framework which allows to construct an algebraic representation of sums and reduce them.
OPE at null infinity (20' + 10')30m
We will provide a new subleading collinear expansion of flat space amplitudes in the Mellin basis, which will make contact with the OPE of the dual theory at null infinity. Assuming the existence of highest-weight representation for the OPE, we will derive a recursion relation for the coefficients of the subleading collinear expansion based on the extended BMS algebra which includes also singular supertranslations. The outcome is that not only the leading OPE coefficient is determined by the asymptotic symmetries at null infinity but also the subleading coefficients at first order in the holomorphic expansion. Various examples of OPE from scattering amplitudes of massless particles will be discussed.
On-shell heavy particle effective theories (20' + 10')30m
We introduce on-shell variables for Heavy Particle Effective Theories (HPETs) with the goal of extending Heavy Black Hole Effective Theory to higher spins and of facilitating its application to higher post-Minkowskian orders. These variables inherit the separation of spinless and spin-inclusive effects from the HPET fields, resulting in an explicit spin-multipole expansion of the three-point amplitude for any spin. By matching amplitudes expressed using the on-shell HPET variables to those derived from the one-particle effective action, we find that the spin-multipole expansion of a heavy spin-s particle corresponds exactly to the multipole expansion (up to order 2s) of a Kerr black hole, that is, without needing to take the infinite spin limit. Finally, we show that tree-level radiative processes with same-helicity bosons emitted from a heavy spin-s particle exhibit a spin-multipole universality.
1-loop correction to radiative black hole scattering (20' + 10')30m
I will be presenting a bootstrap method of determining the one-loop amplitude integrand for 2-2 scattering of massive scalars, mediated by Yang-Mills with one emitted gluon. The integrand is determined using color-kinematics relations and symmetry considerations of kinematic numerator dressings, as well as generalized unitarity cuts. Double-copy construction leads immediately to the associated massive-scalar scattering correction with radiation in axion-dilaton gravity for free.
The two-loop all-plus gluon amplitude (20' + 10')30m
I report on the computation of the planar two-loop all-plus gluonic amplitude at arbitrary multiplicity. The all-plus helicity configuration admits considerable simplifications in its computation, and closed forms for the divergent and polylogarithmic finite parts of this amplitude were determined previously. It is possible to obtain these two-loop contributions via an effective one-loop approach. The last part needed for the complete planar amplitude is the two-loop rational terms, which are currently only known for up to seven gluons. We believe that a similar effective one-loop calculation should suffice to obtain these rational terms. For this we make use of the six-dimensional spinor helicity formalism.
Geometrical aspects of integrability in two dimensions and Toda models (20' + 10')30m
Massive integrable quantum field theories in two dimensions have been largely studied in the past through an axiomatic procedure called S-matrix bootstrap. Such approach, although it allows to find exact values for the S-matrix elements, is cryptic in its principles and a full connection with standard perturbation theory is still lacking. I will address the problem from a lagrangian point of view; starting from a general lagrangian, by the only requirement that all the non-elastic amplitudes need to be null at the tree-level, I will reconstruct what couplings are allowed to obtain an integrable model. In this way a geometric construction naturally emerges from properties of the scattering and a connection between higher dimensional root polytopes and on-shell Feynman diagrams can be highlighted. The cancellation mechanism between diagrams contributing to non-allowed processes can then be explained from the only properties of roots and structure constants of the underlying Lie algebras.
Harmonic analysis for multi-point conformal blocks (20' + 10')30m
The aim is to approach the problem of computing multi-point conformal blocks for Null Polygon Wilson Loops in N=4 SYM through harmonic analysis as in 1612.02479, where conformal blocks appear as wave functions of Calogero-Sutherland models. We start from tackling the problem of standard multi-point conformal blocks in one dimension, which will then be a key example for extensions in higher dimensions and the NPWL case, where further constraints due to null conditions come into play.
Two-mass contributions to polarized three-loop operator matrix elements (20' + 10')30m
In the study of deep-inelastic scattering, the operator matrix elements are important ingredients for the matching relations in the variable flavour number scheme and for the calculation of Wilson coefficients in the asymptotic regime Q2» mc, mb. I will report on the analytic calculation of the polarized two mass
OMEs ∆A(3) gg,Q and ∆APS,(3) Qq to three loops, with an emphasis on the mathematical structures which arise in the result.
The double copy of massive scalar QCD (20' + 10')30m
I will discuss the reconstruction of the effective action of the gravitational theory emerging from the double-copy of massive scalar quantum chromodynamics. The resulting theory consists of massive scalar fields, graviton, dilaton and a two-form. We work out the emerging Lagrangian explicitly up to the sixth order in scalar fields and propose an all order form. In the case where the number of flavours is 1 and the matter scalar is massless, the Lagrangian has an enhanced global SL(2,R) symmetry.
(Humboldt University Berlin)
Subleading soft dressing and asymptotic symmetries (20' + 10')30m
Feynman diagram calculations in theories with massless particles suffer from infrared divergences. It is well-known that their occurrence can be associated to the assumption of free states in the asymptotics and thereby the disregard of long-range effects of interactions mediated by massless particles. In the dressed state formalism one incorporates these effects and obtains finite S-matrix elements. This procedure was related to the existence of asymptotic symmetries in the theory. I will review these developments and discuss dressed states at subleading order in the soft momentum expansion and the associated subleading soft theorems.
Exhibition planning6h 45m
11:15 - 12:15: Progress Report
Each subgroup summarizes the status of their exhibit.
(10 minutes each, including discussion)
12:15 - 14.30: Content Session
To refine the message of each exhibit (includes lunch)
Goal of this session: The working groups will
a) Discuss in detail the content of their exhibit and develop texts.
b) Check with other groups if messages mesh into overall concept, agree on final headlines, write final texts
14:30 - 16:30: Design Session
To refine the form of each exhibit (includes a coffee break)
The working groups identify areas of each exhibit that require further work and solve any problems, build models, draw sketches of individual elements, identify & test appropiate coding tools
16:30 - 17:30: Realisation Session
Building and programming the exhibits
Make a matrix of all tasks required to realize your exhibit, note if it can be done by the group and assign group members to each task, including who should contact external entities if it requires external input. Assign a time to each task to get a timeline for realisation.
17:30 - 18:00: Present refined exhibits
Each group summarizes the work of the day.
The session will focus on the skills required by the ESRs to film and edit high-quality video footage in order to take part fully in the ESR film project. Topics covered will include:
• Legal aspects of making documentaries: film agreements, author rights, ethics aspects.
• Dramaturgy and storytelling through practical exercises.
• Introduction to cameras, lenses, sound and lighting.
• Editing and post-production.
This workshop will include:
• Answering difficult questions; dealing with difficult audience members
• Blanking out while presenting and how to recover
• Time management during a talk (slide design and how to skip ahead)
• Preparing slide sets from scratch based on storytelling structure
Observation: Participants will receive an SD card and verbal feedback on their informal in-class presentations.