Triangle Seminars
Tuesday, 27 Jan 2026
Deep Learning based discovery of Integrable Systems
📍 London
Evgeny Sobko
(LIMS)
Abstract:
Integrable systems are exactly solvable models that play a central role in QFT, string theory and statistical physics offering an ideal setting for understanding complex physical phenomena and developing novel analytical methods. However, the discovery of new integrable systems remains a major open challenge due to the nonlinearity of the Yang–Baxter equation (YBE) that defines them, and the vastness of its solution space. Here we present the first AI-based framework that enables the discovery of new quantum integrable systems in exact analytical form. Our
method combines an ensemble of neural networks, trained to identify high-precision numerical solutions to the YBE, with an algebraic extraction procedure based on the Reshetikhin integrability condition, which reconstructs the corresponding Hamiltonian families analytically. When applied to spin chains with three- and four-dimensional site spaces, we discover hundreds of previously unknown integrable Hamiltonians. Remarkably, these Hamiltonians organize into rational algebraic varieties, and we conjecture that this rationality holds universally — revealing a previously unexplored connection between quantum integrability and algebraic geometry. By unlocking inte-
grable systems far beyond the reach of traditional methods, this AI-driven approach substantially
expands the landscape of exactly solvable models and opens a scalable path to further discoveries.
Integrable systems are exactly solvable models that play a central role in QFT, string theory and statistical physics offering an ideal setting for understanding complex physical phenomena and developing novel analytical methods. However, the discovery of new integrable systems remains a major open challenge due to the nonlinearity of the Yang–Baxter equation (YBE) that defines them, and the vastness of its solution space. Here we present the first AI-based framework that enables the discovery of new quantum integrable systems in exact analytical form. Our
method combines an ensemble of neural networks, trained to identify high-precision numerical solutions to the YBE, with an algebraic extraction procedure based on the Reshetikhin integrability condition, which reconstructs the corresponding Hamiltonian families analytically. When applied to spin chains with three- and four-dimensional site spaces, we discover hundreds of previously unknown integrable Hamiltonians. Remarkably, these Hamiltonians organize into rational algebraic varieties, and we conjecture that this rationality holds universally — revealing a previously unexplored connection between quantum integrability and algebraic geometry. By unlocking inte-
grable systems far beyond the reach of traditional methods, this AI-driven approach substantially
expands the landscape of exactly solvable models and opens a scalable path to further discoveries.
Posted by: Sebastian Cespedes
Wednesday, 28 Jan 2026
Relativistic Field Theories for Interacting Classical Higher-Spin Particles
📍 London
Radu Roiban
(Penn State University)
Abstract:
The construction of an effective field theory describing the long-distance interactions of Kerr black holes remains elusive.
As a step in its direction, we discuss relativistic effective field theories (EFT) designed to capture the long-distance gravitational interactions of massive spinning particles. While "no-go" theorems severely constrain the formulation of interacting higher-spin theories, we argue that these challenges can be navigated in the classical limit through the use of spin coherent states.
These states naturally incorporate gapless excitations which turn out to provide a description for processes in which the magnitude of the spin vector evolves dynamically.
By appropriately choosing the couplings of the theory these modes can either be decoupled, as we show by analyzing 3-point, Compton, and two-body amplitudes, or tuned to describe specific systems. We discuss the broader applicability of this framework, showing that it captures certain supersymmetric black holes as well as the dynamics of Newtonian bound states under external probes. Finally, we discuss possible strategies to identify the definition of Kerr black holes in this framework.
The construction of an effective field theory describing the long-distance interactions of Kerr black holes remains elusive.
As a step in its direction, we discuss relativistic effective field theories (EFT) designed to capture the long-distance gravitational interactions of massive spinning particles. While "no-go" theorems severely constrain the formulation of interacting higher-spin theories, we argue that these challenges can be navigated in the classical limit through the use of spin coherent states.
These states naturally incorporate gapless excitations which turn out to provide a description for processes in which the magnitude of the spin vector evolves dynamically.
By appropriately choosing the couplings of the theory these modes can either be decoupled, as we show by analyzing 3-point, Compton, and two-body amplitudes, or tuned to describe specific systems. We discuss the broader applicability of this framework, showing that it captures certain supersymmetric black holes as well as the dynamics of Newtonian bound states under external probes. Finally, we discuss possible strategies to identify the definition of Kerr black holes in this framework.
Posted by: Jesse van Muiden
New Bounds on Null Energy in Quantum Field Theories
📍 London
Andrew Rolph
(Vrije U., Brussels)
Abstract:
Energy plays a ubiquitous role in physics. Many physical classical field theories obey pointwise energy conditions, and these have played an important role in, for example, singularity theorems. However, for local, relativistic quantum field theories (QFTs), the study of energy is both richer and more precarious. In this talk, I will derive new families of quantum null energy inequalities (QNEIs), i.e. bounds on integrated null energy, in QFTs in two and higher dimensions. These are universal, state-independent lower bounds on semi-local integrals of the energy-momentum flux in a null direction, and the first of this kind for interacting theories in higher dimensions. Our ingredients include the quantum null energy condition (QNEC), strong subadditivity of von Neumann entropies, defect operator expansions, and the vacuum modular Hamiltonians of null intervals and strips. These results are new, fundamental constraints on null energy in quantum field theories.
Energy plays a ubiquitous role in physics. Many physical classical field theories obey pointwise energy conditions, and these have played an important role in, for example, singularity theorems. However, for local, relativistic quantum field theories (QFTs), the study of energy is both richer and more precarious. In this talk, I will derive new families of quantum null energy inequalities (QNEIs), i.e. bounds on integrated null energy, in QFTs in two and higher dimensions. These are universal, state-independent lower bounds on semi-local integrals of the energy-momentum flux in a null direction, and the first of this kind for interacting theories in higher dimensions. Our ingredients include the quantum null energy condition (QNEC), strong subadditivity of von Neumann entropies, defect operator expansions, and the vacuum modular Hamiltonians of null intervals and strips. These results are new, fundamental constraints on null energy in quantum field theories.
Posted by: Andrew Svesko
Thursday, 29 Jan 2026
Novel properties of QFTs with long-range interactions
📍 London
Luke Lippstreu
(Edinburgh)
Abstract:
Infrared divergences obscure key analytic properties of scattering amplitudes, exposing gaps in our understanding of unitarity, causality, and crossing symmetry in theories with long-range forces. In this talk, I will use a simple model to illustrate novel analytic features of long-range theories, including modifications to the connectedness structure of amplitudes and to the general optical theorem. Since the LSZ reduction formula does not apply to theories with long-range forces, I will also present a modified version of LSZ reduction for this model, which accounts for long-range interactions and yields IR-finite amplitudes without ambiguous scales or ill-defined integrals.
Infrared divergences obscure key analytic properties of scattering amplitudes, exposing gaps in our understanding of unitarity, causality, and crossing symmetry in theories with long-range forces. In this talk, I will use a simple model to illustrate novel analytic features of long-range theories, including modifications to the connectedness structure of amplitudes and to the general optical theorem. Since the LSZ reduction formula does not apply to theories with long-range forces, I will also present a modified version of LSZ reduction for this model, which accounts for long-range interactions and yields IR-finite amplitudes without ambiguous scales or ill-defined integrals.
Posted by: Nathan Moynihan