Solving N=4 super-Yang-Mills theory via Scattering Amplitudes: January 8, 2024 – March 8, 2024

Participant ListView Videos

Organizing by:

  • Benjamin Basso (Ecole Normale Superieure),
  • Lance Dixon (SLAC/Stanford U.)
  • Jaroslav Trnka (UC Davis)
  • Anastasia Volovich (Brown)

This program will bring together physicists and mathematicians with expertise in different facets of particle scattering in planar N=4 super-Yang-Mills theory, in order to try to solve the theory for generic values of the coupling and kinematical variables.

It has been a long-standing quest to solve strongly-interacting four-dimensional relativistic quantum field theories by analytical methods. N = 4 super-Yang-Mills theory (SYM) is the “hydrogen atom” of gauge theories. It is the archetype for the AdS/CFT correspondence, connecting it to string theory and gravity, particularly at strong coupling. Perturbatively, its gluon scattering amplitudes closely resemble those for the gauge theory of the strong interactions, quantum chromodynamics (QCD). Hence it has proven indispensable as a testing ground for powerful new computational methods for precision collider physics. In the planar limit of a large number of colors (gauge group SU(Nc) with Nc → ∞), N = 4 SYM is integrable, and its scattering amplitudes are dual to the expectation values of Wilson loops for closed light-like polygons. The perturbative expansion of planar N = 4 SYM has remarkable geometric features, centered around polytopes related to various Grassmannians and the
differential forms that live on them.

There are currently three independent descriptions of scattering amplitudes in planar N = 4 SYM, illustrated in the figure.

A weak-coupling formulation makes contact with perturbative methods involving Feynman diagrams; a “holographic” strong-coupling formulation employs minimal-area surfaces in Anti-de Sitter space; and a pentagon operator product expansion (POPE) approach exploits the two-dimensional integrability of a dual string picture at finite coupling in various kinematic limits. These formulations are all mutually consistent. (Indeed the compatibility of the POPE and perturbative approaches can be established through eight loop orders.) But they are formulated in mathematically very distinct ways, based on different underlying physical principles, and they make different properties of amplitudes manifest. In this program, the goal is to find a unified description of amplitudes in this theory that matches onto each of these formulations in the appropriate limit. Mathematically, the proposal is to search for functions that are able to interpolate between weak and strong coupling, for arbitrary kinematics, using all the knowledge we have about them in the respective limits. In this way one could gain a quantitative picture of how weak coupling excitations (gluons) evolve into strong coupling ones (strings) under a variety of physical circumstances.  The spin-off for QCD could also be very important.

This program also has an associated workshop: Mathematical Aspects of N=4 Super-Yang-Mills Theory: February 26-March 1, 2024


WEEK 1: January 8 – January 10, 2024
Speaker: Lauren Williams
Title: The positive (tropical) Grassmannian, the amplituhedron, and cluster algebras

WEEK 2: January 10 – January 12, 2024
Speaker: Clément Dupont
Title: Motivic coaction for periods and amplitudes

WEEK 3: January 15 – January 17, 2024
Speaker: Lionel Mason
Title: Strong Coupling and Minimal Surfaces

WEEK 4: January 22 -January 24, 2024
Speaker: Nima Arkani-Hamed
Title: Geometry, Cluster Algebras and All That

WEEK 5: January 29 – January 31, 2024
Speaker: Mark Spradlin
Title: Landau Singularities and Symbol Alphabets

WEEK 6: February 5 – February 7, 2024
Speaker: Amit Sever
Title: Pentagon OPE and Other Roads to Solving Planar N=4

WEEK 7: February 12 – February 14, 2024
Speaker: Lance Dixon
Title: Amplitude Bootstrap and Antipodal Duality

WEEK 8: February 19 – February 21, 2024
Speaker: James Drummond
Title: TBA

WEEK 9: February 26 – March 1, 2024
Workshop: Mathematical Aspects of N=4 Super-Yang-Mills Theory

WEEK 10: March 4 – March 8, 2024
Speaker: Luis Alday
Title: TBA