Week 11.04.2022 – 17.04.2022

With a view towards constructing Calabi Yau manifolds, we present some rudiments of the intersection between algebraic, differential and arithmetic geometry. Throughout we will take the opposite of the Bourbaki approach and work through explicit examples, rather than to emphasise on the theory.

Consistency with quantum gravity can impose non-trivial constraints at low energies, even if the Planck scale is at very high energy. The Swampland program aims to determine the constraints that an effective field theory must satisfy to be consistent with a UV embedding in a quantum gravity theory. One of the most important swampland conditions is the presence of infinite towers of states becoming massless at the weak coupling/large field limits. This has been extensively tested in string theory compactifications, but a bottom-up explanation was missing. In this talk I will provide a possible explanation based on finiteness of black hole entropy. I will also explain how several wampland criteria, including the Weak Gravity Conjecture, Distance Conjecture and bounds on the finiteness of the quantum gravity vacua, may be more fundamentally a consequence of the finiteness of quantum gravity amplitudes.

The quantum Church-Turing thesis would imply that there is a unique model of quantum computing. It follows that quantum computers could simulate quantum field theories efficiently.After a review on the simulation of topological quantum field theories, we will focus on a lattice approach to conformal field theories from anyonic chains.; it will be possible to follow this talk online (please register at https://london-tqft.co.uk)

QCD undergoes a transition from the confined phase (hadron gas) to a deconfined quark-gluon plasma at a temperature of about 155 MeV. This phenomenon can be investigated in relativistic heavy-ion experiments and studied theoretically, using e.g. simulations of QCD discretised on a space-time lattice. In this talk, I will review some aspects of QCD at nonzero temperature, with an emphasis on results obtained by our lattice QCD collaboration. Very recently, machine learning has been introduced as a new tool to study lattice field theory. In the final part, I will present some results of applications of machine learning to phase transitions in statistical field theory.

We study Chern-Simons theories at large N with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines ending on fundamentals. We classify the conformal line operators along an arbitrary smooth path as well as the spectrum of conformal dimensions and transverse spins of their boundary operators at finite 't Hooft coupling. These line operators are shown to satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two line operators. We argue that this equation together with the spectrum of boundary operators are sufficient to uniquely determine the expectation values of these operators. We demonstrate this by bootstrapping the two-point function of the displacement operator on a straight line. We show that the line operators in the theory of bosons and the theory of fermions satisfy the same evolution equation and have the same spectrum of boundary operators. ----- Part of the London Integrability Journal Club. If you are a new participant please register at integrability-london.weebly.com. Link emailed on Tuesday.