2021-22 Series
- 18 and 25 October 2021: Chris Herzog, What is an anomaly?
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- 25 October and 1 November 2021: David Vegh, (Holographic) Fermi surfaces
In this lecture, we present a few elementary facts about Fermi surfaces, then discuss how to find interesting ``non-Fermi liquids'' via the AdS/CFT correspondence. We study different backgrounds (e.g. AdS, BTZ, and Reissner-Nordstrom), and the wave-equation of probe fields on top of these geometries. We discuss how to compute boundary two-point functions by solving the bulk equations and then explore the results.
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- 1 and 8 November 2021: Andreas Fring, CPT symmetry in quantum field theory
CPT-symmetry is a fundamental symmetry of nature that is respected by all physical processes. It consists of a consecutive reversal of time (T), reflection of space at an arbitrary point (Parity P) and a charge conjugation that replaces particles by antiparticles. I briefly discuss the role P T -symmetry plays in quantum mechanics and how it may be utilised for a consistent formulation of non-Hermitian theories. For a relativistic quantum field theory the CPT-theorem provides the general framework for the validity of this symmetry to occur, by stating that the CPT-symmetry is equivalent to a strong reflection and a simultaneous Hermitian conjugation. In this lecture I will prove the theory in the framework of a Lagrangian quantum field theory for spin 0, 1 and spin 1/2 Dirac fields, by first identifying the separate transformation and a subsequent combination. Subsequently these transformations are used to identify the behaviour of various interaction terms under their action. I conclude by commenting on the experimental observations of CP-symmetry violation in the neutral K-meson decay.
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- 8 and 15 November 2021: Nadav Drukker, An Introduction to Observables in Gauge Theories
Gauge theories are ubiquitous in theoretical physics, not to mention that the standard model is one. It is therefore of utmost importance to know what the observables of these theories are, quantities that can be calculated and measured. I start with a long discussion based on the most familiar gauge theory, Maxwell's electromagnetism, where a lot of computations can be done explicitly. I then take the lessons from that to non-abelian gauge theories. The observables covered are local, Wilson loops, and briefly 't Hooft loops and surface operators.
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- 15 and 22 November: Chris Hull, Duality Symmetry in String Theory
This lecture provides an introduction to duality symmetries in string theory.
String theory was originally formulated as a theory of strings propagating in space time with interactions governed by the string coupling constant g. Scattering amplitudes for small g were constructed as a perturbation theory in g. Five consistent supersymmetric string theories were found, all in 10 spacetime dimensions with five distinct perturbation theories. This left many questions unanswered, such as why there should be five apparently consistent quantum theories of gravity and what happens to these theories as the coupling constant is increased.
Such questions were answered by the developments in the mid-1990s that have been called the 2nd superstring revolution. Dualities proved to be the key to uncovering the non-perturbative structure of superstring theory and in particular its strong coupling behaviour. When g is large, one can analyse the theory as a perturbation theory in 1/g and seek a “dual theory” with coupling constant g’ whose perturbative expansion in g’ matches the behaviour of the original theory as a perturbation theory in 1/g on identifying g’=1/g. In some cases the dual theory is again a string theory, which might be a different string theory from the original one. In other cases, the dual theory isn’t a string theory at all, but a new theory – M-theory. This leads to a picture in which all 5 string theories are related by dualities and so are all seen as different limits of M-theory. Duality transformation provide new symmetries of string/M theory and T,S and U-dualities. Remarkably, the theory that emerges Is no longer just a theory of strings but one which includes both strings and branes which are higher dimensional extended objects. As the branes are related to strings by duality symmetries, they should be regarded as being on the same footing as the strings and of equal importance.
The lecture explores all of these issues and discusses some examples.
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- Februaty 21 - March 14 2022: Damián Galante, On the SYK Model and the Emergence of Spacetime
Time and Location: Mondays at 10:30 at the London Institute for Mathematical Sciences, 21 Albemarle St.
In these lectures, we will present two 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.
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- March 21 - April 11 2022: Yang-Hui He, A Playful Introduction to Some Modern Geometry
Time and Location: Mondays at 10:30 at the London Institute for Mathematical Sciences, 21 Albemarle St.
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.
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- TBA