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Amplitudes 2017 Summer School

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Lecture Theatre 2 (Appleton Tower)

Lecture Theatre 2

Appleton Tower

11 Crichton Street, Edinburgh, EH8 9LE, UK
Description
The study of scattering amplitudes has developped substantially over the past few years, with applications ranging from precision calculations for the LHC through new approaches to gauge theories and gravity and ending with pure mathematics. The annual meeting Amplitudes 2017 workshop will be hosted by the Higgs Centre between 10-14 July. This present summer school is held in the week preceding the workshop, and it offers an introduction to some of the central topics to be discussed at the workshop. Five lecturers will deliver sets of lectures and tutorials over the full 5 days of 3-7 July.
  • Monday, 3 July
    • 10:15 → 10:45
      Registration 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 10:50 → 11:00
      Welcome 10m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 11:00 → 11:50
      1001 tales of gluons - lecture 1 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Stefan Weinzierl (University of Mainz)
      Video
    • 12:00 → 12:50
      Multiloop Scattering Amplitudes and Cluster Algebras - lecture 1 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Marcus Spradlin (Brown University)
      Video
    • 13:00 → 14:30
      Lunch Break 1h 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 14:30 → 15:20
      1001 tales of gluons - lecture 2 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Stefan Weinzierl (University of Mainz)
      Video
    • 15:30 → 16:00
      Coffee break 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 16:00 → 16:50
      Multiloop Scattering Amplitudes and Cluster Algebras - lecture 2 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Marcus Spradlin (Brown University)
      Video
    • 17:00 → 17:20
      Coffee break 20m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 17:20 → 17:45
      Azurite: finding master Integrals using algebraic geometry 25m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      For any given Feynman graph, the set of integrals with all possible powers of the propagators spans a vector space of finite dimension. I will introduce the package Azurite (arXiv:1612.04252) which efficiently finds a basis of this vector space. It constructs the needed integration-by-parts (IBP) identities on a set of generalized- unitarity cuts. It is based on syzygy computations and analyses of the symmetries of the involved Feynman diagrams and is powered by the computer algebra systems Singular and Mathematica. I will also discuss some recent progresses and application of Azurite.
      Speaker: Alessandro Georgoudis (Uppsala University)
      Mathematica Notebook
      Slides
      Video
    • 17:50 → 18:15
      Amplitudes and Correlator Integrands to Ten Loops Using Graphical Bootstraps 25m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      We introduce the "triangle" and "pentagon" rules for obtaining contributing coefficients to the four-point correlation function and scattering amplitude integrands in planar, maximally supersymmetric Yang-Mills theory. Combining these graphical rules with the rung rule prove powerful enough to fully determine both functions through ten loops. We illustrate their applications, compare their relative strengths for fixing coefficients, and if time permits, survey some of the novel features of the higher-loop expressions.
      Speaker: Vuong-Viet Tran (Durham University)
      Slides
      Video
    • 18:20 → 19:30
      Welcome reception 1h 10m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
  • Tuesday, 4 July
    • 09:30 → 10:20
      1001 tales of gluons - lecture 3 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Stefan Weinzierl (University of Mainz)
      Video
    • 10:30 → 11:00
      Coffee break 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 11:00 → 11:50
      1001 tales of gluons - tutorial 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Video
    • 12:00 → 12:50
      Multiloop Scattering Amplitudes and Cluster Algebras - lecture 3 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Marcus Spradlin (Brown University)
      Video
    • 13:00 → 14:30
      Lunch break 1h 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 14:30 → 15:20
      1001 tales of gluons - lecture 4 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Stefan Weinzierl (University of Mainz)
      Video
    • 15:30 → 16:00
      Coffee break 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 16:00 → 16:50
      Multiloop Scattering Amplitudes and Cluster Algebras - lecture 4 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Marcus Spradlin (Brown University)
      Video
    • 17:00 → 17:20
      Coffee break 20m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 17:20 → 17:45
      Maximal Cuts in Arbitrary Dimension 25m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      After recalling the basics of generalized unitarity and maximal cuts, I will discuss recent work with Mads S{\o}gaard and Yang Zhang (1704.04255): We discuss a procedure for computing maximal cuts in general D dimensions, based on the Baikov representation which simplifies the structure of the cuts. In our procedure, for a given topology, the integration splits into several regions and the number of independent regions is equal to the number of master integrals for the topology. The functions thus obtained inherit IBP and dimension shift identities from the uncut integral. Moreover, the functions, corresponding to the master integrals, obtained from the different regions, form the Wronskian matrix for the system of differential equations on the maximal cut. The discussion will be guided by an explicit example (probably the massless double box, but this remains to be decided).
      Speaker: Jorrit Bosma (ETH, Zurich)
      Slides
      Video
    • 17:50 → 18:15
      Combinatorics and Topology of Kawai–Lewellen–Tye Relations 25m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      We study surprising connections between algebraic topology and string theory amplitudes which underlie Kawai–Lewellen–Tye (KLT) relations. For instance, we show that entries of the inverse KLT kernel can be understood as intersection numbers of certain cycles. In the field-theory limit, combinatorics of these intersections gives rise to the bi-adjoint scalar theory.
      Speaker: Sebastian Mizera (Perimeter Institute for Theoretical Physics)
      Slides
      Video
  • Wednesday, 5 July
    • 09:30 → 10:20
      Graphical Methods for Sharp Prediction: from theories entirely formal to the utterly effective - lecture 1 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: John Joseph Carrasco (CEA, Saclay)
      Lectures
      Slides
      Video
    • 10:30 → 11:00
      Coffee break 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 11:00 → 11:50
      Graphical Methods for Sharp Prediction: from theories entirely formal to the utterly effective - lecture 2 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: John Joseph Carrasco (CEA, Saclay)
      Video
    • 12:00 → 12:50
      Grassmannian Geometry of Scattering Amplitudes - lecture 1 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Jaroslav Trnka (University of California, Davis)
      Video
    • 13:00 → 14:30
      Lunch break 1h 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 14:30 → 15:20
      Grassmannian Geometry of Scattering Amplitudes - lecture 2 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Jarosalav Trnka (University of California, Davis)
      Video
    • 15:30 → 16:00
      Coffee break 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 16:00 → 16:50
      Feynman Integrals - lecture 1 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Johannes Henn (Mainz University)
    • 17:00 → 17:20
      Coffee break 20m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 17:20 → 17:45
      Two-Loop Fundamental Colour-Kinematics Duality 25m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      The study of loop-level scattering amplitudes in (super-)Yang-Mills theories has seen enormous progress over the last decade or so. Unfortunately, many of these developments are limited to the planar limit which consists of only planar Feynman diagrams. Meanwhile, loop-level (super-)gravity amplitudes are difficult to calculate with ordinary Feynman diagrams. In this talk I will introduce Bern, Carrasco & Johansson’s (BCJ’s) colour-kinematics duality. The duality recycles planar tree-level amplitudes into full-colour loop- level amplitudes, while also giving loop-level gravity amplitudes by a double copy. I will also discuss the inclusion of fundamental matter multiplets, and apply these techniques to N=2 supersymmetry with extra hypermultiplets at two loops.
      Speaker: Gustav Mogull (University of Edinburgh)
      Slides
      Video
    • 17:50 → 18:15
      Unifying Relations for Scattering Amplitudes 25m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      The talk is based on 1612.00868 and work to appear with Clifford Cheung and Congkao Wen. We derive new scattering amplitudes relations which reveal a hidden unity among theories of diverse spins in general spacetime dimensions. These relations are built from a set of Lorentz invariant differential operators which transmute states of higher spin into states of lower spin. Transmutation takes amplitudes of gravity coupled to a dilaton and two-form into any amplitude in Einstein- Yang-Mills, the special Galileon, and (Dirac-)Born-field theory. Starting from Yang-Mills amplitudes, the transmutation covers any amplitude in gauged bi-adjoint scalar theory and the non-linear sigma model. As a corollary, known properties of gauge theory and gravity amplitudes like the Weinberg soft theorems, color-kinematics duality, the KLT relations, and the CHY construction are trivially inherited by the transmuted amplitudes. In the case of the non-linear sigma model, the recently found kinematic algebra becomes obvious from this construction.
      Speaker: Chia-Hsien Shen (Caltech)
      Slides
      Video
  • Thursday, 6 July
    • 09:30 → 10:20
      Feynman Integrals - lecture 2 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Johannes Henn (Mainz University)
    • 10:30 → 11:00
      Coffee break 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 11:00 → 11:50
      Feynman Intergrals - tutorial 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Johannes Henn (Mainz University)
    • 12:00 → 12:50
      Graphical Methods for Sharp Prediction: from theories entirely formal to the utterly effective - lecture 3 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: John Joseph Carrasco (CEA, Saclay)
      Video
    • 13:00 → 14:30
      Lunch break 1h 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 14:30 → 15:20
      Grassmannian Geometry of Scattering Amplitudes - lecture 3 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Jaroslav Trnka (University of California, Davis)
      Video
    • 15:30 → 16:00
      Coffee break 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 16:00 → 16:50
      Feynman Integrals - lecture 3 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Johannes Henn (Mainz University)
    • 17:00 → 17:20
      Coffee break 20m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 17:20 → 17:45
      Determining the Soft Anomalous Dimension from General Constraints 25m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Bootstrapping techniques---wherein one imposes known constraints on an ansatz in the hope of uniquely determining the answer---have proven to be an increasingly powerful method for computing amplitudes in recent years. While the most significant progress in this direction has been made in planar maximally supersymmetric Yang- Mills theory, these techniques can be naturally extended to the types of quantities directly relevant to collider computations. One place these methods show particular promise is in the resummation of large logarithms, and we here report the successful bootstrap of the (correction to the all-order dipole contribution) of the massless soft anomalous dimension at three loops, up to an overall numerical factor.
      Speaker: Andrew McLeod (SLAC, Stanford University)
      Slides
      Video
    • 17:50 → 18:15
      Exploring Reggeon bound states in strongly coupled N=4 super Yang- Mills theory 25m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      I will discuss scattering amplitudes in strongly coupled N=4 super Yang-Mills theory in the multi-Regge limit. In the strong coupling regime, the calculation of the scattering amplitudes reduces to the solution of a system of non-linear, coupled integral equations through the AdS/CFT-correspondence. These equations reduce to standard Bethe ansatz equations in the multi-Regge limit. In this kinematical regime, scattering amplitudes in N=4 SYM are physically described by bound states of effective particles, the so-called Reggeons. The six- point remainder function is fully described by a two-Reggeon bound state and is known at finite coupling. At eight external gluons a three-Reggeon bound state starts to appear about which much less is known. We investigate the three-Reggeon bound state in the strong coupling regime and try to make some generalisations to multiple-Reggeon bound states.
      Speaker: Theresa Abl (ETH, Zurich)
      Slides
      Video
    • 19:15 → 22:30
      Dinner 3h 15m Royal Scots Club

      Royal Scots Club

      arrive 19.15-19.30

  • Friday, 7 July
    • 09:30 → 10:20
      Grassmannian Geometry of Scattering Amplitudes - lecture 4 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Jaroslav Trnka (University of California, Davis)
      Video
    • 10:30 → 11:00
      Coffee break 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 11:00 → 11:50
      Grassmannian Geometry of Scattering Amplitudes - tutorial 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Jaroslav Trnka (University of California, Davis)
      Video
    • 12:00 → 12:50
      Graphical Methods for Sharp Prediction: from theories entirely formal to the utterly effective - lecture 4 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: John Joseph Carrasco (Institute for Theoretical Physics (IPhT), CEA-Saclay and University of Paris-Saclay)
      Video
    • 13:00 → 14:30
      Lunch break 1h 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 14:30 → 15:20
      Feynman Integrals - lecture 4 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Johannes Henn (Mainz University)
    • 15:30 → 16:00
      Coffee break 30m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 16:00 → 16:50
      Feynman Integrals - lecture 5 50m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      Speaker: Johannes Henn (Mainz University)
    • 17:00 → 17:20
      Coffee break 20m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
    • 17:20 → 17:45
      On-shell diagrams and Ambitwistor strings in N=8 supergravity 25m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      I will discuss how on-shell diagrams for N=4 Super Yang Mills can be extended to N=8 Supergravity, giving Grassmannian integral formulae for tree-level amplitudes. I will then describe the connection between these formulae and equivalent expressions for the same amplitudes arising from ambitwistor string theory.
      Speaker: Joe Farrow (Durham University)
      Video
    • 17:50 → 18:15
      From BCJ double copy to inflationary cosmology 25m Lecture Theatre 2

      Lecture Theatre 2

      Appleton Tower

      11 Crichton Street, Edinburgh, EH8 9LE, UK
      The BCJ double copy relates the scattering amplitudes from gauge and gravity theories. One such theory corresponds to a model first developed by Volkov and Akulov to describe Goldstone fermions (associated with spontaneous supersymmetry breaking). It was later realized that the Volkov-Akulov model is equivalent to the same constrained (nilpotent) superfields appearing in the cosmological models known as alpha-attractors. In this talk I'll explore some possible applications of the double copy procedure to inflationary cosmology.
      Speaker: Andres Luna-Godoy (University of Glasgow)
      Slides
      Video
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