Related papers: Integrability for Feynman Integrals
We propose a double-scaling limit of $\beta$-deformed ABJM theory in three-dimensional $\mathcal{N} = 2$ superspace, and a non-local deformation thereof. Due to the regular appearance of the theory's Feynman supergraphs, we refer to this…
The Symmetries of Feynman Integrals (SFI) is a method for evaluating Feynman Integrals which exposes a novel continuous group associated with the diagram which depends only on its topology and acts on its parameters. Using this method we…
The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is…
This is an introductory survey written in Japanese on classical integrability from the viewpoint of symmetry reduction of 4-dimensional anti-self-dual Yang-Mills equations. Twistor construction methods are discussed in detail in…
We propose that Baxter's Z-invariant six-vertex model at the rational gl(2) point on a planar but in general not rectangular lattice provides a way to study Yangian invariants. These are identified with eigenfunctions of certain monodromies…
The scattering-matrix for planar Yang-Mills with N=4 supersymmetry relies on the assumption that integrability holds to all orders in perturbation theory. In this note we define a map from the spectral variables x^{\pm}, parameterizing the…
We study the remnants of Yangian symmetry of AdS/CFT magnons reflecting from boundaries with no degrees of freedom. We present the generalized twisted boundary Yangian of open strings ending on boundaries which preserve only a subalgebra h…
We consider theories consisting of a planar interface with $\N=4$ super-Yang-Mills on either side and varying gauge coupling across the interface. The interface does not carry any independent degrees of freedom, but is allowed to support…
In this dissertation, we discuss how our understanding of the large-N spectrum of AdS/CFT has been deepened by integrability-based approaches. We begin with a comprehensive review of the integrability of the gauge theory spin-chain and that…
We establish a connection between time evolution of free Fermi droplets and partition function of \emph{generalised} \emph{q}-deformed Yang-Mills theories on Riemann surfaces. Classical phases of $(0+1)$ dimensional unitary matrix models…
The reflection matrices of multi magnon bound states are obtained explicitely by exploiting the Yangian symmetry of boundary scattering on the Y=0 maximal giant graviton brane.
An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman…
This course on Feynman integrals starts from the basics, requiring only knowledge from special relativity and undergraduate mathematics. Topics from quantum field theory and advanced mathematics are introduced as they are needed. The course…
We study the commutative limit of the non-commutative maximally supersymmetric Yang-Mills theory in four dimensions (N=4 SYM). The commutative limits of non-commutative spaces are important in particular in the applications of…
For correlators in $\mathcal{N}=4$ Super Yang-Mills preserving half the supersymmetry, we manifestly recast the gauge theory Feynman diagram expansion as a sum over dual closed strings. Each individual Feynman diagram maps on to a Riemann…
Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with…
The superspace flatness conditions which are equivalent to the field equations of supersymmetric Yang-Mills theory in ten dimensions have not been useful so far to derive non trivial classical solutions. Recently, modified flatness…
A new class of two dimensional integrable field theories, based on the mathematical notion of Poisson manifolds, and containing gravity-Yang-Mills systems as well as the G/G gauged Wess-Zumino Witten-model, are presented. The local…
The Fourier transform of two-point momentum-space Feynman integrals with massless propagators and two off-shell legs can be used to prove identities between their periods, exemplified by the glue-and-cut identity. We generalize this…
I describe how integrable quantum field theories in 2 spacetime dimensions are characterized by infinite dimensional quantum group symmetries, namely the q-deformations of affine Lie algebras, and their Yangian limit. These symmetries can…