This workshop gives a flavour of where and how different types of symmetries are employed in the modern context of quantum theories. The workshop will cover the interplay between discrete (CPT) and continuous Lie group symmetries. For instance, conformal symmetries in the form of infinite-dimensional Virasoro in quantum field theories, Kac-Moody algebras in the study of string sigma-models, Lorentzian Kac-Moody algebras (e.. E11) in the description of string and brane theories, and quantum group symmetries in the study of integrable systems. Speakers: Andrea Cavaglia (King's College London) Anastasia Doikou (Heriot-Watt University, Edinburgh) Valentina Forini (City, University of London) Vidas Regelskis (University of Hertfordshire and Vilnius University) Takanobu Taira (City, University of London) Peter West (King's College London) https://cityagm.weebly.com/

Concepts from quantum information theory have become increasingly important in our understanding of entanglement in QFTs. One prominent example of this is the modular Hamiltonian, which is closely related to the Unruh effect. Using complex analysis, we determine this operator for the chiral fermion at finite temperature on the circle and show that it exhibits surprising new features. This simple system illustrates how a modular flow can transition from complete locality to complete non-locality, thus bridging the gap between previously known limits. We derive the first exact results for the entropy in the different spin sectors, and comment on the analytic continuation of the Rényi entropies to the complex plane.

Postponed due to strike

I will discuss recent developments in constructions of 5d N=1 supersymmetric gauge theories and their UV fixed points, which are strongly-coupled SCFTs. The lectures will start with some background on 5d gauge theories, their Coulomb branch and effective action, as well as their constructions in M-theory on non-compact Calabi-Yau threefolds. In the second lecture I will discuss some new developments of various groups in the past year.

Motivated by extending the parameter space of the Standard Model of Particle Physics, I will describe how to understand the effects of an imaginary mixing mass term in a non-Hermitian but PT-symmetric extension of scalar QED. The classical theory is already not trivial, and requires a new interpretation of the equations of motion, Noether's theorem and gauge invariance. The path integral can be defined with appropriate field variables, and a consistent picture emerges, opening the way for potential alternative descriptions of the Higgs sector.

Isolated systems consisting of many interacting particles are generally assumed to relax to a stationary equilibrium state whose macroscopic properties are described by the laws of thermodynamics and statistical physics. Time crystals, as first proposed by Wilczek, could defy some of these fundamental laws and for instance display persistent non-decaying oscillations. They can be engineered by external driving or contact with an environment, but are believed to be impossible to realize in isolated many-body systems. I will show that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not relax to stationarity and hence constitutes a genuine time crystal that does not rely on external driving or coupling to an environment. I will trace this phenomenon to the existence of periodic extensive quantities and find their frequency to be a no-where continuous (fractal) function of the anisotropy parameter of the chain.

We consider the continuous symmetry properties of non-Hermitian, PT-symmetric quantum field theories. We begin by revisiting the derivation of Noether’s theorem and find that the conserved currents of non-Hermitian theories correspond to transformations that do not leave the Lagrangian invariant. After describing the implications of this conclusion for gauge invariance, we consider the spontaneous breakdown of global and local symmetries, and illustrate how the Goldstone theorem and the Englert-Brout-Higgs mechanism are borne out. We conclude by commenting on the potential avenues for model building in fundamental physics from the non-Hermitian deformation of the Standard Model of particle physics.

In this talk, based on the work to appear, we present an alternative representation of the conformal block with external scalars in general spacetime dimensions in terms of a finite summation over Appell fourth hypergeometric function, and its generalization to the primary operator exchange with continuous spin which is relevant for Lorentzian spacetime. Using these results we apply the Lorentzian inversion formula to compute so-called crossing kernel in general spacetime dimensions, and the result can be written as a double infinite summation over certain Kempe de Feriet hypergeometric functions. During the talk, we will introduce various physical quantities and discuss their subtitles and applications.

We test various conjectures on quantum gravity with general 6d string compactifications in the framework of F-theory. Starting with a gauge theory coupled to gravity, we first analyze the limit in Kähler moduli space where the gauge coupling tends to zero while gravity is kept dynamical. A key observation is made about the appearance of a tensionless string in such a limit. For a more quantitative analysis, we focus on a U(1) gauge symmetry and determine the elliptic genus of this string in terms of certain meromorphic weak Jacobi forms, of which modular properties allow us to determine the charge-to-mass ratios of certain string excitations. A tower of these asymptotically massless charged states are then confirmed to satisfy the (sub-)Lattice Weak Gravity Conjecture, the Completeness Conjecture, and the Swampland Distance Conjecture. We interpret their charge-to-mass ratios in two a priori independent perspectives. All of this is then generalized to theories with multiple U(1)s. If time permits, we will also briefly report on our more recent 4-dimensional story.

Scattering amplitudes are one of most important class of physical observables in quantum field theories. Over the last decade or so, there has been a lot of activities regarding the computation of scattering amplitudes in a wide range of interesting theories, where extremely powerful new frameworks for studying scattering amplitudes have emerged, known as the modern S-matrix program. In this talk I will review some of these powerful techniques, and discuss their applications. The applications will mostly focus on effective field theories, that include twistor-like formulas for scattering amplitudes of world-volume theories of probe D-brane and M5 brane, amplitude constraints on effective field theories, such as supersymmetric non-renormalization theorems, unitarity bounds on low-energy spectra.