Registration Room: Lecture Theatre 2

Welcome Room: Lecture Theatre 2

1001 tales of gluons - lecture 1

• Stefan Weinzierl (University of Mainz)

Room: Lecture Theatre 2

Multiloop Scattering Amplitudes and Cluster Algebras - lecture 1

• Marcus Spradlin (Brown University)

Room: Lecture Theatre 2

1001 tales of gluons - lecture 2

• Stefan Weinzierl (University of Mainz)

Room: Lecture Theatre 2

Multiloop Scattering Amplitudes and Cluster Algebras - lecture 2

• Marcus Spradlin (Brown University)

Room: Lecture Theatre 2

Azurite: finding master Integrals using algebraic geometry

• Alessandro Georgoudis (Uppsala University)

Room: Lecture Theatre 2 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.

Amplitudes and Correlator Integrands to Ten Loops Using Graphical Bootstraps

• Vuong-Viet Tran (Durham University)

Room: Lecture Theatre 2 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.

1001 tales of gluons - lecture 3

• Stefan Weinzierl (University of Mainz)

Room: Lecture Theatre 2

1001 tales of gluons - tutorial Room: Lecture Theatre 2

Multiloop Scattering Amplitudes and Cluster Algebras - lecture 3

• Marcus Spradlin (Brown University)

Room: Lecture Theatre 2

1001 tales of gluons - lecture 4

• Stefan Weinzierl (University of Mainz)

Room: Lecture Theatre 2

Multiloop Scattering Amplitudes and Cluster Algebras - lecture 4

• Marcus Spradlin (Brown University)

Room: Lecture Theatre 2

Maximal Cuts in Arbitrary Dimension

• Jorrit Bosma (ETH, Zurich)

Room: Lecture Theatre 2 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).

Combinatorics and Topology of Kawai–Lewellen–Tye Relations

• Sebastian Mizera (Perimeter Institute for Theoretical Physics)

Room: Lecture Theatre 2 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.

Graphical Methods for Sharp Prediction: from theories entirely formal to the utterly effective - lecture 1

• John Joseph Carrasco (CEA, Saclay)

Room: Lecture Theatre 2

Graphical Methods for Sharp Prediction: from theories entirely formal to the utterly effective - lecture 2

• John Joseph Carrasco (CEA, Saclay)

Room: Lecture Theatre 2

Grassmannian Geometry of Scattering Amplitudes - lecture 1

• Jaroslav Trnka (University of California, Davis)

Room: Lecture Theatre 2

Grassmannian Geometry of Scattering Amplitudes - lecture 2

• Jarosalav Trnka (University of California, Davis)

Room: Lecture Theatre 2

Feynman Integrals - lecture 1

• Johannes Henn (Mainz University)

Room: Lecture Theatre 2

Two-Loop Fundamental Colour-Kinematics Duality

• Gustav Mogull (University of Edinburgh)

Room: Lecture Theatre 2 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.

Unifying Relations for Scattering Amplitudes

• Chia-Hsien Shen (Caltech)

Room: Lecture Theatre 2 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.

Feynman Integrals - lecture 2

• Johannes Henn (Mainz University)

Room: Lecture Theatre 2

Feynman Intergrals - tutorial

• Johannes Henn (Mainz University)

Room: Lecture Theatre 2

Graphical Methods for Sharp Prediction: from theories entirely formal to the utterly effective - lecture 3

• John Joseph Carrasco (CEA, Saclay)

Room: Lecture Theatre 2

Grassmannian Geometry of Scattering Amplitudes - lecture 3

• Jaroslav Trnka (University of California, Davis)

Room: Lecture Theatre 2

Feynman Integrals - lecture 3

• Johannes Henn (Mainz University)

Room: Lecture Theatre 2

Determining the Soft Anomalous Dimension from General Constraints

• Andrew McLeod (SLAC, Stanford University)

Room: Lecture Theatre 2 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.

Exploring Reggeon bound states in strongly coupled N=4 super Yang- Mills theory

• Theresa Abl (ETH, Zurich)

Room: Lecture Theatre 2 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.

Grassmannian Geometry of Scattering Amplitudes - lecture 4

• Jaroslav Trnka (University of California, Davis)

Room: Lecture Theatre 2

Grassmannian Geometry of Scattering Amplitudes - tutorial

• Jaroslav Trnka (University of California, Davis)

Room: Lecture Theatre 2

Graphical Methods for Sharp Prediction: from theories entirely formal to the utterly effective - lecture 4

• John Joseph Carrasco (Institute for Theoretical Physics (IPhT), CEA-Saclay and University of Paris-Saclay)

Room: Lecture Theatre 2

Feynman Integrals - lecture 4

• Johannes Henn (Mainz University)

Room: Lecture Theatre 2

Feynman Integrals - lecture 5

• Johannes Henn (Mainz University)

Room: Lecture Theatre 2

On-shell diagrams and Ambitwistor strings in N=8 supergravity

• Joe Farrow (Durham University)

Room: Lecture Theatre 2 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.

From BCJ double copy to inflationary cosmology

• Andres Luna-Godoy (University of Glasgow)

Room: Lecture Theatre 2 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.