Week 31.10.2021 – 06.11.2021

Lonti Autumn 2021 Series: Lecture 2. Live Tutorial. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. Abstract: 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.

Lonti Autumn 2021 Series: Lecture 3. Release of Recorded Lecture. Available at https://youtu.be/zABaRs1Ghmw 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.

The Ryu-Takayanagi formula and its generalizations have led to a surprising amount of progress in our understanding of quantum gravity in the last fifteen years, culminating in the recent derivation of the Page curve in toy models of evaporating black holes. However, we still don’t understand why these formulas are true from a canonical point of view. In this talk, I will attempt to make progress on this problem by developing an analogy between gravitational entropy formulas in low-dimensional examples of holography and similar-looking formulas that have appeared in the study of entanglement entropy in emergent gauge theories. This talk will be based on 1807.06575, 2107.11872, and 2107.12634.

I will cover some of the most recent developments on classical spinning black holes and their perturbations. The reinterpretation of them in terms of a classical limit of QFT three-point amplitudes, where the black hole is modeled as a massive spinning particle, sheds light on many fundamental properties such as integrability, the Newman-Janis construction, and the so-called classical double copy relating the solution to gauge theory.

It has been a long-standing conjecture that any CFT with a large central charge and a large gap M in the spectrum of single-trace operators must be dual to a local effective field theory in AdS. In my talk, I will discuss a proof of a sharp form of this conjecture. In particular, I will explain how to derive numerical bounds on bulk Wilson coefficients in terms of M using the conformal bootstrap. The bounds exhibit scaling in M expected from dimensional analysis in the bulk. The main technical tools are dispersive CFT sum rules. These sum rules provide a dictionary between CFT dispersion relations and S-matrix dispersion relations in appropriate limits. This dictionary allows one to apply recently-developed flat-space methods to construct positive CFT functionals. My talk will be based on https://arxiv.org/pdf/2106.10274.pdf, which is joint work with S. Caron-Huot, L. Rastelli, and D. Simmons-Duffin.

Over the past decade we have witnessed the emergence of a plethora of correspondences between QFTs in various dimensions arising from higher dimensional SCFTs. In this talk I will overview another strategy to produce correspondences building upon geometric engineering techniques. As applications I will touch upon higher DT theory for Calabi-Yau 3-folds, the algebra of G(2) instantons, and generalizations of level/rank dualities.

TBA

t.b.a. ---- 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.