Related papers: On the bootstrap structure of Yangian-invariant fa…
We initiate the S-matrix bootstrap analysis of theories with non-invertible symmetries in (1+1) dimensions. Our previous work showed that crossing symmetry of S-matrices in such theories is modified, with modification characterized by the…
We attempt to systematically derive tree-level scattering amplitudes in four-dimensional, planar, maximally supersymmetric Yang-Mills theory from integrability. We first review the connections between integrable spin chains, Yangian…
Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the k deformations associated to the more general q deformations but with…
We show that the recently found S-matrices describing the scattering of two-particle bound states of the light-cone string sigma model on AdS5 x S5 are compatible with Yangian symmetry. In case the invariance with respect to the centrally…
Using unitarity methods, we compute, for several massive two-dimensional models, the cut-constructible part of the one-loop 2->2 scattering S-matrices from the tree-level amplitudes. We apply our method to various integrable theories,…
A free boson on a lattice is the simplest field theory one can think of. Its partition function can be easily computed in momentum space. However, this straightforward solution hides its integrability properties. Here, we use the methods of…
We establish a direct connection between scattering amplitudes in planar four-dimensional theories and a remarkable mathematical structure known as the positive Grassmannian. The central physical idea is to focus on on-shell diagrams as…
Tree-level scattering amplitudes in planar N=4 super Yang-Mills are known to be Yangian-invariant. It has been shown that integrability allows to obtain a general, explicit method to find such invariants. The uplifting of this result to the…
The bootstrap programme for finding exact S-matrices of integrable quantum field theories with N=1 supersymmetry is investigated. New solutions are found which have the same fusing data as bosonic theories related to the classical affine…
Two outer automorphisms of infinite-dimensional representations of $sl(2)$ algebra are considered. The similar constructions for the loop algebras and yangians are presented. The corresponding linear and quadratic $R$-brackets include the…
We describe new constructions of the infinite-dimensional representations of $U(\mathfrak{g})$ and $U_q(\mathfrak{g})$ for $\mathfrak{g}$ being $\mathfrak{gl}(N)$ and $\mathfrak{sl}(N)$. The application of these constructions to the quantum…
The planar scattering amplitudes of $\mathcal{N} = 4$ super-Yang--Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at…
Planar N=4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also…
We perform a detailed study of the Yangian symmetry of smooth supersymmetric Maldacena-Wilson loops in planar N=4 super Yang-Mills theory. This hidden symmetry extends the global superconformal symmetry present for these observables. A…
Similarity transformations and eigenvalue relations of monodromy operators composed of Jordan-Schwinger type L matrices are considered and used to define Yangian symmetric correlators of n-dimensional theories. Explicit expressions are…
In the realm of contemporary physics, the bootstrap method is typically associated with an optimization-based approach to problem-solving. This method leverages our understanding of a specific physical problem, which is used as the…
It is known that the Yangian of PSU(2,2|4) is a symmetry of the tree-level S-matrix of N=4 super Yang-Mills. On the other hand, the complete one-loop dilatation operator in the same theory commutes with the level-one Yangian generators only…
We compute the decomposition of representations of Yangians into g-modules for simply-laced Lie algebras g. The decomposition has an interesting combinatorial tree structure. Results depend on a conjecture of Kirillov and Reshetikhin.
In this article, we reconsider the formulation of Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory, and we investigate to what extent this symmetry lifts to the beta/gamma-deformation of the model. We first apply cohomology…
We present a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. The new formula for the scattering of n particles is given by an integral over the position of n…