Triangle Seminars

Abstract:
The Kerr-Schild double copy (KSDC) is well-known for relating exact classical solutions between Yang-Mills theory and theories of gravity. However, whether this correspondence provides a more fundamental mapping between the underlying symmetries of gauge theory and gravity remains an underdeveloped area of research in the contemporary double copy program. In this paper, we demonstrate that the KSDC correspondence does not provide a mapping between the residual symmetry structures of the Kerr-Schild ansatz in Yang-Mills theory and gravity. On the gauge theory side, residual symmetries form an infinite-dimensional algebra of functions along null directions. On the gravitational side, residual diffeomorphisms preserving the Kerr-Schild form of the Schwarzschild metric generate a conformal algebra on S^{2}, which decomposes into Killing vectors and proper conformal Killing vectors (CKVs). While the Killing sector reproduces the expected global isometries, the CKV sector yields an infinite-dimensional algebra after imposing asymptotic flatness and horizon regularity. This appears to contradict the fact that the Schwarzschild solution admits no proper conformal symmetries. We resolve this apparent contradiction by constructing a Weyl-compensated BRST complex, showing that the CKV sector is BRST-exact and therefore trivial in cohomology, so that the physical symmetry algebra reduces to the global isometries of Schwarzschild. This demonstrates that the KSDC introduces an enlarged symmetry structure at the level of the ansatz, but preserves physical symmetries after a cohomological reduction, revealing a fundamental mismatch between Yang-Mills and gravity at the level of residual symmetries.

Abstract:
In the presence of extended defects, familiar incoming particles can scatter into exotic outgoing states created by twist operators. We show that the fundamental mechanism driving these ”categorical scattering” processes is the presence of localized ’t Hooft anomalies on the defect’s worldvolume. Defect anomalies trap non-trivial charges at junctions between the symmetry lines and the interface, opening new transmission channels that would naively appear to violate selection rules. This mechanism can be applied to several (1+1)d systems, including massless fermions, integrable massive field theories, and lattice spin chains.

Abstract:
Many local conformal field theories can be analytically continued to a family of nonlocal, long-range CFTs by varying the exponent of the kinetic term \((p^2)^{\zeta}\) in the action away from the usual \(\zeta=1\). It is natural to then ask what singles out the original local CFT within each such family. The answer is neat – it has the most degrees of freedom, as counted by the (universal part of the) sphere free energy, also sometimes called the central charge. This provides a simple organising principle for models such as the critical Ising and O(N) vector CFTs in any d, and a compact way of organising perturbative data for their scaling dimensions. For unitary CFTs, this extremum is a maximum, which can be proven in conformal perturbation theory. In this talk, I will first give an introduction to nonlocal CFTs, then discuss counting degrees of freedom in CFTs, and finally prove the main result.

Abstract:
Talk info can be found on https://lims.ac.uk/event/a-simpler-cosmology/

Observations of the universe on the largest and smallest accessible scales have revealed surprising simplicity. In contrast, the most popular theoretical frameworks predicted a slew of new particles, forces and dimensions on the tiniest, subatomic scales, and a chaotic multiverse on the greatest. The observations should make us reconsider our assumptions. Might there be better explanations for the basic properties of the universe? I’ll outline a new, simpler unified paradigm, based on the known laws of physics and CPT symmetry, which explains (i) the large-scale geometry of the universe and the primordial density perturbations, without inflation, (ii) the dark matter as a right handed neutrino, without any other BSM particle, (iii) why there are three generations of elementary particles, without strings. The new picture provides clues about quantum gravity, the big bang and the arrow of time as well as a potential resolution of the gauge-gravity hierarchy puzzle.

Abstract:
Massless spinning cosmological correlators are highly nontrivial and their structure is still poorly understood. I will show that four-point correlators can be dramatically simplified using a novel geometric object: the Cosmological Grassmannian. This framework makes key properties manifest—such as symmetries, factorization, and the flat-space limit—and reveals the hidden simplicity of these correlators.

Abstract:
AI for Mathematical Sciences (AIMS) seminar series

String theory is a surprisingly complex structure which harbours some of the largest mathematical data sets. While this makes string theory a rich and fertile ground for theoretical and mathematical physics it also presents a major challenge when attempting to relate string theory to known particle physics. I will present an informal introduction to string theory and explain how modern computational methods, particularly machine learning techniques, can be used to overcome some of these challenges. This includes supervised machine learning methods to understand mathematical data within string theory, heuristic searches using techniques such as reinforcement learning and genetic algorithms to explore the string `landscape' and self-supervised learning to solve differential equations.

To subscribe for the AIMS series please fill out the form https://applications.lims.ac.uk/subscribe-to-aims

Abstract:
The Laser Interferometer Space Antenna (LISA) is an ESA-NASA mission adopted in 2024 and expected to be launched in 2035. LISA is the definitive probe of the millihertz gravitational-wave spectrum, populated by massive black hole binaries, extreme mass-ratio inspirals, compact Galactic binaries, and perhaps cosmological sources. Extracting all of these signals from the signal-rich, confused-limited LISA data stream presents major computational and statistical challenges, both fundamental and practical. AI and ML techniques (such as simulation-based inference and neural emulators) have recently attracted significant interest in our community because of their potential efficiency, generality, and flexibility. I will discuss how these methods could be applied to LISA data analysis for tasks of detection, parameter estimation, detector characterization, and waveform generation. I will focus on how AI can complement traditional matched-filtering and MCMC-based pipelines, and I will highlight potential pitfalls and limitations.