SEMPS Schedule

Arrival & Coffee 10:30 - 11:00

Yangian symmetry, GKZ equations and integrable Feynman graphs

Fedor Levkovich-Maslyuk (City University, London)

Abstract: We extend the powerful property of Yangian invariance to a new large class of conformally invariant multi-loop Feynman integrals. This leads to new highly constraining differential equations for them, making integrability visible at the level of individual Feynman graphs. Our results apply to planar Feynman diagrams in any spacetime dimension dual to an arbitrary network of intersecting straight lines on a plane (Baxter lattice), with propagator powers determined by the geometry. The graphs we consider determine correlators in the recently proposed "loom" fishnet CFTs. The construction unifies and greatly extends the known special cases of Yangian invariance to likely the most general family of integrable scalar planar graphs. We also relate these equations in certain cases to famous GKZ (Gelfand-Kapranov-Zelevinsky) hypergeometric operators, opening the way to using new powerful solution methods.

Boundary integrability in massless AdS3

Vasileios Moustakis (University of Surrey)

Abstract: In recent years, integrability techniques have been successfully applied to the study of the AdS/CFT dualities to obtain exact results on both sides the correspondence. In this talk, we will focus on the boundary integrability problem of AdS3xS3xT4 string theory. One of its novel characteristics, which differentiates it from its higher dimensional counterparts, is the presence of two types of massless excitations in the gauge-fixed worldsheet theory.

We will discuss the integrable reflection matrices, describing the reflection of those massless excitations off of the string endpoints, and their corresponding boundary subalgebras for singlet and vector representations. Time permitting, we can also demonstrate how the boundary algebraic Bethe ansatz can be applied to this integrable system, as a natural next step in tits development.

Lunch 12:40 - 14:00

From data to the analytic S-matrix

Andrea Guerrieri (City University, London)

Abstract: In this talk I will discuss our recent attempt (https://arxiv.org/pdf/2410.23333) of understanding the QCD spectrum using the available experimental data. To do so, we developed a fit strategy that combines the S-matrix Bootstrap with non-convex optimization methods, and applied our algorithm to the case of \pi\pi scattering. The fitted amplitude correctly predicts the low energy ChiPT behavior, the experimental total cross sections at higher energy, and the physical spectrum up to 1.4 GeV. Surprisingly, Bootstrap predicts an additional tetraquark state, not yet observed, and that is being investigated in the decay of the B+ -> pi+ p+ pi- at LHCb.

Chiral Conformal Field Theories 

Nivedita (Oxford)

Abstract: Conformal Field Theories (CFTs) occupy an intermediate and crutial position between Topological Quantum Field Theories (TQFTs), which are rmathematically relatively well understood, and general Quantum Field Theories (QFTs), for which a rigorous non-perturbative formulation remains elusive. Two-dimensional chiral CFTs are closely related to three-dimensional TQFTs by a bulk-boundary correspondence, with 2D Wess–Zumino–Witten (WZW) model and its associated 3D Chern–Simons theory being the most well studied example. Unitary chiral CFTs admit three distinct mathematical formulations: in terms of unitary Vertex Operator Algebras (VOAs), Conformal Nets, and the Segal (functorial) approach, where they appear as projective representations of the conformal cobordism category. We discuss progress toward constructing a fully extended functorial field theory description of chiral CFTs, focusing on assignment to points and circles.

Tea 15:40 - 16:10

Graph Cosmohedra

Ross Glew (University of Hertfordshire)

Abstract: The associahedron is a polytope whose boundary stratification captures the combinatorial structure of non-overlapping chords of an n-gon. Its vertices are labeled by full triangulations, while its facets correspond to individual chords. A natural generalization of this is to consider the structure of non-overlapping sub-polygons, which also gives rise to a polytope known as the cosmohedron. The facets of the cosmohedron are labeled by partial triangulations of the n-gon, and its vertices correspond to nested polyangulations. Both the associahedron and the cosmohedron have received attention in the physics literature due to their relevance to scattering amplitudes and the flat space wavefunction of trace phi^3 theory. For any simple graph G, there exists a generalisation of the associahedron, known as the graph associahedron, which is constructed by considering tubes and tubings of G. The classical associahedron is recovered as the graph associahedron for the path graph. In this talk, we explore how the concept of cosmohedra can be generalised to arbitrary graphs, leading to a family of polytopes we refer to as graph cosmohedra. We will investigate the construction of these polytopes in terms of tubing concepts on graphs and provide explicit embeddings for them.