Week 27.02.2022 – 05.03.2022

In these lectures, we will present to seemingly different theories. The first one is a theory of gravity in two dimensions, called Jackiw-Teitelboim (JT) gravity, that is relevant in the context of higher-dimensional, near-extremal black holes. The second one is a quantum mechanical theory of fermions, with no gravity, called the Sachdev, Ye and Kitaev (SYK) model. We will explore precisely how JT gravity emerges from the SYK model by studying their actions, correlation functions and thermodynamic properties. This constitutes the simplest toy model of what theoretical physicists now call the holographic principle. Address: 21 Albemarle St, London W1S 4BS Floor 2: London Institute of Mathematical Sciences (LIMS)

Scattering amplitudes of elementary particles exhibit a fascinating simplicity, which is entirely obscured in textbook Feynman-diagram computations. While these quantities find their primary application to collider physics, describing the dynamics of the tiniest particles in the universe, they also characterise the interactions among some of its heaviest objects, such as black holes. Violent collisions among black holes occur where tremendous amounts of energy are emitted, in the form of gravitational waves. 100 years after having been predicted by Einstein, their extraordinary direct detection in 2015 opened a fascinating window of observation of our universe at extreme energies never probed before, and it is now crucial to develop novel efficient methods for highly needed high-precision predictions. Thanks to their inherent simplicity, amplitudes are ideally suited to this task. I will begin by reviewing the computation of a very familiar quantity Newton's potential, from scattering amplitudes and unitarity. I will then explain how to compute directly observable quantities such as the scattering angle for light or for gravitons passing by a heavy mass such as a black hole. These computations are further simplified thanks to a remarkable, yet still mysterious connection between scattering amplitudes of gluons (in Yang-Mills theory) and those of gravitons (in Einstein's General relativity), known as the "double copy", whereby the latter amplitudes can be expressed, schematically, as sums of squares of the former -- a property that cannot be possibly guessed by simply staring at the Lagrangians of the two theories. I will conclude by discussing the prospects of performing computations in Einstein gravity to higher orders in Newton's constant using a new, gauge-invariant version of the double copy, and as an example I will briefly discuss the computation of the scattering angle for classical black hole scattering to third post-Minkowskian order (or O(G^3) in Newton's constant G).

I will review recent progress in the study of a class of integrable deformations of sigma models known as "homogeneous Yang-Baxter". These deformations can be understood as generalisations of the well known TsT transformations. In fact, rather than deformations, the homogeneous Yang-Baxter procedure too can be reinterpreted as imposing twisted worldsheet boundary conditions in the undeformed sigma model. I will explain how to construct the twist in the generic case, which generalises the twist of TsT from abelian to non-abelian. I will also use the expression for the twist to discuss the construction of the classical spectral curve in some examples. To conclude, I will mention some open questions related to the quantum integrability of these models. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

After a brief introduction to some of the impact which integrable methods and the Bethe ansatz have had on the study of the AdS/CFT correspondence in string theory, we will focus on the axiomatic approach to S-matrix theory in 1+1 dimensions. We will highlight the issues that arise when the particles are massless, and how this is in fact connected to Zamolodchikov's way of describing two-dimensional conformal field theories by means of integrability techniques. We will then mention how the axiomatic approach extends to form-factors, which are the gate to access the n-point functions of the theory. If time permits, we will briefly depict how this finds a contemporary application in the area of the AdS_3/CFT_2 correspondence; part of London TQFT Journal Club (please register at https://london-tqft.vercel.app);