This series consists of talks in the area of Quantum Fields and Strings.
In effective field theory, causality fixes the signs of certain interactions. I will describe how these Lorentzian constraints are encoded in the Euclidean theory, and use the conformal bootstrap to derive analogous causality constraints in CFT. Applied to spinning fields, these constraints include (some of) the Hofman-Maldacena bounds derived from conformal collider physics. I will also discuss applications to holographic theories.
For a CFT perturbed by a relevant operator, the entanglement entropy of a spherical region may be computed as a perturbative expansion in the coupling. A similar perturbative expansion applies for excited states near the vacuum. I will describe a method due to Faulkner for calculating these entanglement entropies, and apply it in the limit of small sphere size. The motivation for these calculations is a recent proposal by Jacobson suggesting an equivalence between the Einstein equation and the "maximal vacuum entanglement hypothesis" for quantum gravity.
I will describe ongoing work with Miguel Paulos, Joao Penedones, Jon Toledo and Balt van Rees. We are attempting to bootstrap massive quantum field theories.
We formulate a massive S-matrix bootstrap which we analyze both numerically and analytically. We confront our findings with the conformal theory results of lecture 1. We will derive analytic bounds for the couplings in massive 2d QFTs and observe that the Ising field theory with magnetic field lies precisely at the boundary of these bounds. We conclude with higher dimensional speculations.
I will describe ongoing work with Miguel Paulos, Joao Penedones, Jon Toledo and Balt van Rees. We are attempting to bootstrap massive quantum field theories.
A massive quantum field theory can be put in a large AdS space, i.e. in a box. Its correlators define, as they approach the boundary, a conformal theory. The bootstrap of the latter can pose strong constraints on the former as we will describe. We will then initiate a presentation of the general and of the peculiar features of S-matrices in two dimensions.
The BPS spectrum of d=4 N=2 field theories in general contains not only hyper and vector-multipelts but also short multiplets of particles with arbitrarily high spin. These BPS states of higher spin reveal quite a peculiar behavior, so sometimes they are called "wild"
states. In this talk we would try to discuss a small refinement of the asymptotic study (spectral network technique) of tt* equations arising in an effective theory on 2d defects in N=2 4d SYM theory capturing spin information and apply it to study some properties of wild BPS spectra.
I will present a new area law in General Relativity. This new area law holds on local analogues of event horizons that have an independent thermodynamic significance due to the Bousso bound. I will also discuss a quantum generalization of this more local notion of thermodynamics.
We compute the scaling dimensions of a large class of disorder operators ("monopoles") in the planar limit of CS-fermion theories. The lightest such operator is shown to have dimension (2/3) k^{3/2}, where k is the CS level. The computation is based on recently developed techniques for solving CS-matter at all 't Hooft couplings, and the operator dimensions are obtained by finding complex saddles in the low-temperature phase of the CS-fermion path integral in a monopole background. We will also discuss the implications of this result to 3D bosonization dualities.