Name: Amplitudes, Motives and Beyond
Start: 2015-05-26T08:00:00+02:00
End: 2015-06-12T18:00:00+02:00
Location: Mainz Institute for Theoretical Physics Johannes Gutenberg University

Monday, May 25, 2015
Tuesday, May 26, 2015
10:55 AM Welcome - Stefan Weinzierl
Welcome
- Stefan Weinzierl
10:55 AM - 11:00 AM
Room: 02.430
11:00 AM Multiple polylogarithms in cyclotomic fields and subfields - David Broadhurst
Multiple polylogarithms in cyclotomic fields and subfields
- David Broadhurst
11:00 AM - 11:45 AM
Room: 02.430 Single-scale Feynman diagrams evaluate to periods that may (but need not) be multiple polylogarithms with arguments in algebraic number fields, such as Nth roots of unity, with N=1,2,6 being prominent. In this introductory talk I shall give examples of such evaluations and give evidence for some new conjectures, in real subfields of cyclotomic fields, that have emerged from recent discussion with Pierre Deligne. I hope to pursue the latter as the workshop progresses.
4:00 PM Elliptic multiple zeta values and superstring one-loop amplitudes, part I - Oliver Schlotterer
Elliptic multiple zeta values and superstring one-loop amplitudes, part I
- Oliver Schlotterer
4:00 PM - 4:40 PM
Room: 02.430 In the first half of this talk, we introduce elliptic multiple zeta values (eMZVs) as iterated integrals on a genus-one curve and illustrate their natural appearance in one-loop scattering amplitudes of the open superstring. The underlying elliptic iterated integrals are shown to require an infinite alphabet of differential forms subject to a rich network of shuffle- and (so-called) Fay-relations. Based on these identities, any worldsheet integral in the low-energy expansion of one-loop open superstring amplitudes can be expressed in terms of eMZVs. We conclude with an overview of eMZVs indecomposable under Fay and shuffle relations.
4:45 PM Elliptic multiple zeta values and superstring one-loop amplitudes, part II - Johannes Broedel
Elliptic multiple zeta values and superstring one-loop amplitudes, part II
- Johannes Broedel
4:45 PM - 5:25 PM
Room: 02.430 The second half of the talk opens up a new perspective on eMZVs based on their dependence on the modular parameter of the elliptic curve. A differential equation gives rise to an alternative description of eMZVs in terms of iterated integrals over Eisenstein series. The resulting counting of indecomposable eMZVs ties in with Fay and shuffle relations and leads to selection rules among the occurring iterated Eisenstein integrals. When formulated in terms of non-commutative variables, these selection rules reproduce all known commutator relations from an algebra of special derivations on a free Lie algebra.
Wednesday, May 27, 2015
11:00 AM Yangian invariant scattering amplitudes as unitary matrix integrals - Matthias Staudacher
Yangian invariant scattering amplitudes as unitary matrix integrals
- Matthias Staudacher
11:00 AM - 11:45 AM
Room: 02.430 I show how to derive the deformed Yangian invariant tree level amplitudes from the quantum inverse scattering method. The construction naturally leads to deformed Graßmannian contour integrals. The novelty of our construction is that the contours are fixed from the beginning. In the split helicity case the contours correspond to the manifolds of the unitary groups, and the contour integration is just invariant Haar integration. The resulting integrals are analytic functions of the deformation parameters as long as the scattering data is generic, i.e. stays away from collinear configurations. This is joint work with Nils Kanning and Yumi Ko.
4:00 PM The Cluster Bootstrap for Scattering Amplitudes - James Drummond
The Cluster Bootstrap for Scattering Amplitudes
- James Drummond
4:00 PM - 4:40 PM
Room: 02.430 The singularities of scattering amplitudes in planar N=4 super Yang-Mills theory are conjecturally described by a cluster algebra structure. I will present a number of tests of this hypothesis and show that it can be used to determine scattering amplitudes from very little information.
Thursday, May 28, 2015
11:00 AM Periods and Superstring Amplitudes - Stephan Stieberger
Periods and Superstring Amplitudes
- Stephan Stieberger
11:00 AM - 11:45 AM
Room: 02.430 We present (some) connections and implications of superstring amplitudes from and to number theory. These relations include motivic multiple zeta values, single-valued multiple zeta values, Drinfeld, and Deligne associators. More concretely, we will show that tree-level superstring amplitudes provide a beautiful link between generalized multiple Gaussian hypergeometric functions and the decomposition of motivic multiple zeta values. Furthermore, we establish relations between complex integrals on CP^1 minus 3 points as single-valued projection of iterated real integrals on RP^1 minus 3 points. From the the physical point of view this relation expresses closed string amplitudes as projections of open string amplitudes: a relation, which goes far beyond, what is known from the notorious Kawai-Lewellen-Tye (KLT) relations.
Friday, May 29, 2015
11:00 AM Zhegalkin zebra motives - Jan Stienstra
Zhegalkin zebra motives
- Jan Stienstra
11:00 AM - 11:45 AM
Room: 02.430 A Zhegalkin polynomial in n variables is a polynomial function on {F_2}^n; here F_2={0,1} is the field with 2 elements. The zebra with frequency vector v is the F_2 - valued function Z on the plane R^2 defined by the formula Z(x) = floor(2v\cdot x) mod 2. By inserting an n-tuple of zebras into an n-variable Zhegalkin polynomial one obtains an F_2 - valued function F on R^2, which we call a Zhegalkin zebra function. The graph of such a function gives a partion of the plane into black (i.e. F=1) and white (i.e. F=0) areas. This easily produces many beautiful pictures. We will focus on examples for which the picture is a doubly periodic tiling of the plane by black and white convex polygons. These tilings have a very rich geometric structure (including so-called brane tilings or dimer models, Poisson structures, Calabi-Yau manifolds). We focus in particular on examples which reproduce the quantum-periods of the DelPezzo surfaces, and may therefore be considered as mirrors of DelPezzo surfaces.
4:00 PM Calculating Higgs production at three loops in QCD - Falko Dulat
Calculating Higgs production at three loops in QCD
- Falko Dulat
4:00 PM - 4:40 PM
Room: 02.430 I report on our recent calculation of the Higgs cross section at three loops in QCD. I will illustrate how techniques from the study of amplitudes in N=4 can be employed to aid calculations in non-supersymmetric QCD.
Saturday, May 30, 2015
Sunday, May 31, 2015