2023-24 Series
- October 9, 16 and 23 (2023): Neil Lambert, Supergravity a la Fin de Siecle
Time and Location: Mondays at 10:30 at the London Institute for Mathematical Sciences, 21 Albemarle St.
In these lectures we will provide a basic introduction to Supergravity as it arises in String Theory and M-Theory. We will start by introducing vielbeins and spin connections in order to construct supergravity actions. In the secondlecture we will briefly introduce the maximal supergravity theories in ten and eleven-dimensions. We will briefly discuss special holonomy manifolds, explicitly construct BPS p-brane solutions and prove their non-perturbative stability. Time permitting we will discuss toroidal compactifications and U-duality.
I will assume basic MSc level material (Riemannian geometry, fermions and rigid supersymmetry). The lecture notes that will be provided are largely self-contained but the text book “Supergravity” by Freedman and van Proeyen contains more details.
Resources:
- Supergravity a la Fin de Siècle lecture notes: supergravity.pdf (last updated 24 October 2023).
- November 6, 13, 20, 23 (2023): Pau Figueras, The initial (boundary) value problem in numerical general relativity
Time and Location: Mondays at 10:30 at the London Institute for Mathematical Sciences, 21 Albemarle St.
In these series of lectures we will explore initial value problem in general relativity and how it can be solved in a computer in practical situations. We will first cover the necessary mathematical foundations, including the concepts of well-posedness and strong hyperbolicity, and then explore the current formulations of Einstein’s theory of gravity that are implemented in modern numerical codes, namely generalised harmonic coordinates and the BSSN formulation. We shall see how the latter can be implemented in a toy code so as to get some hands on experience. Time permitting, we will also explore the initial boundary value problem in asymptotically anti-de Sitter spaces and how it can be solved in practice using the characteristic formulation of the Einstein equations in applications of holography.
- January 29 and February 5, 12, 19 (2024): Petr Kravchuk, CFTs in Lorentzian signature
Time and Location: Mondays at 10:30 at the London Institute for Mathematical Sciences, 21 Albemarle St.
In these lectures we will discuss various aspects of conformal field theories in Lorentzian signature. First, we will study the general properties of Lorentzian correlation functions, including their global conformal structure and the relation to Euclidean correlators. We will then consider the Regge limit of correlation functions and how this limit requires the introduction of complex spin. We will define complex spin using the Lorentzian inversion formula, and interpret it in terms of non-local light-ray operators. Finally, we will discuss applications of light-ray operators to even shape observables.
- March 4, 5, 12, 18 (2024): Claudia de Rham, Gravity as an Effective Field Theory
This event has been cancelled due to an unforeseen speaker emergency.
Time and Location: 10:30 at the London Institute for Mathematical Sciences, 21 Albemarle St.
Whether we are dealing with gravity, cosmology, particle physics, or exploring signs of new physics at the intersection of multiple fields, Effective Field Theories (EFTs) have become ubiquitous tools to steer our searches for new physics. In these lectures I will start by reviewing the standard EFT approaches, first in the absence of gravity, and establish how consistency of their UV completion can lead to powerful constraints. I will then treat General Relativity as an EFT in its own right and derive the implications for generic gravitational EFTs.
Suggested bibliography:
- Burgess, C.P. Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory. Living Rev. Relativ. 7, 5 (2004). https://doi.org/10.12942/lrr-2004-5
- De Rham, C., Tolley, A. World Scientific Series in Astrophysics, The Encyclopedia of Cosmology, Set 2: Frontiers in Cosmology, Volume 1: Modified Gravity (Nov 2023), https://doi.org/10.1142/13578-vol1 Chapters 1-4.
- Donoghue, J., General relativity as an effective field theory: The leading quantum corrections, Phys.Rev.D50:3874-3888, 1994, https://arxiv.org/abs/gr-qc/9405057.
- April 18 (2 lectures), 22, 25 (2024): Sunil Mukhi, Geodesics and Singularity Theorems in General Relativity
Time and Location: 10:30 at the London Institute for Mathematical Sciences, 21 Albemarle St. On April 18, on top of the morning lecture, there will be an extra lecture early in the afternoon.
These lectures will summarise mathematical aspects of classical General Relativity that are helpful in understanding current developments in the field. Lecture I will focus on Lorentzian-signature geometry, with an emphasis on causal structure. Some topological notions will also be introduced. In Lecture II we will go on to study the behaviour of geodesics in General Relativity and derive the famous Raychaudhuri equation. The null version of this equation, due to Sachs, will also be derived. Lecture III will focus on the "Hawking singularity theorem", namely that cosmological spacetimes with positive local Hubble constant are geodesically incomplete in the past under suitable conditions. In Lecture IV we will discuss the "Penrose singularity theorem" for black holes.
Download the lecture notes here.
Pre-requisites: A first course in General Relativity is essential (e.g. the textbook by James Hartle, Chapters 1-8, 12, 20-21, or by Sean Carroll, Chapters 1-5). Some familiarity with basic topological concepts will be helpful (open/closed sets, compactness, differentiability, vector fields).
References for the course material:
1. General Relativity (Robert M. Wald, Chapters 8 and 9.
2. The large-scale structure of spacetime (Hawking and Ellis), Chapters 6 and 8.
3. Light rays, singularities, and all that (Witten, arXiv:1901.03928), Chapters 3,4,5.