Week 24.10.2022 – 30.10.2022

We will describe the duality between two integrable systems: the 2D Sine-Gordon model and the 2D Thirring model. We will spend some time describing the classical and quantum Sine-Gordon model, in particular its spectrum, S-matrices and underlying quantum-group symmetry. We will then present the duality with the Thirring model as originally stated by Coleman and refined in subsequent literature. All the basic elements will be provided without relying on too many pre-requisites beyond standard graduate-level quantum field theory. The notes comprise a series of exercises.

In my talk I will review the recent progress in non-local infinite derivative gravity theories. The core of the models under investigation is the infinite derivative generalization of the quadratic gravity theory which was first studied in depth by Stelle in 1977. I will explain why unitarity can only be restored for an infinite tower of derivatives. The rest of the talk will concentrate on the cosmological consequences of this non-local gravity proposal for the Starobinsky inflation.

Boundary critical behaviours of systems at bulk criticality have been studied by condensed matter physicists for decades, in the beginning mostly theoretically, then also experimentally. These studies have revealed that the field of boundary critical phenomena is quite rich. For any universality class of bulk critical behaviour usually several distinct universality classes of boundary critical behaviour exist. To elucidate this, we introduce appropriate lattice models and map them onto boundary field theories describing their scale and conformal invariance on large scales. We show that this mapping can be subtle in some cases. We discuss the role and difference of boundary conditions of the field theories on mesoscopic and large scales, to what extent they are characteristic of --- and hence may be used to identify --- the distinct boundary universality classes. Finally, we explain the characteristic near-boundary asymptotic behaviours they exhibit and mention some open problems.

We will review a recent application of Exceptional Field Theory : finding new families of solutions of type IIB supergravity on AdS_4 x S^1 x S^5. To find such solutions, we will compactify type IIB on S^5 x S^1 to obtain a 4d gauged maximal supergravity where new solutions are simply found by extremising a scalar potential. Surprisingly, it is sometime possible to deform our new solutions and break any residual supersymmetry while preserving stability. This is surprising since, from a holographic perspective, these deformations should be dual to non-supersymmetric exactly marginal deformations. We will show that it is a generic behaviour of gravity theories compactified on a circle and we will provide a solution generating technique in terms of a tool called the mapping torus.

One way of probing quantum entanglement is to identify a multi-player task (a “game”) that can be won more reliably when the players share a specific entangled quantum state. I will review some well-known quantum games, and discuss how these can be generalized to games which exploit the entanglement structure of a phase of matter rather than a specific quantum state.