This series consists of talks in the area of Quantum Fields and Strings.
In the context of class S theories and 4D/2D duality relations there, we discuss the skein
relations of general topological defects on the 2D side which is expected to be counterparts
of composite surface-line operators in 4D class S theory. Such defects are geometrically
interpreted as networks in a three dimensional space. We also propose a conjectural com-
putational procedure for such defects in two dimensional SU(N) topological q-deformed
Yang-Mills theory by interpreting it as a statistical mechanical system associated with
We study two-dimensional (4, 4) superconformal field theories of central charge c = 6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap method. This is made possible through a surprising relation between the BPS N = 4 superconformal blocks of c = 6 and bosonic Virasoro conformal blocks of c = 28, and an exact result on the moduli dependence of a certain integrated BPS 4-point function.
I will discuss ongoing work developing Hamiltonian truncation methods for studying strongly-coupled IR physics originating from a perturbed UV conformal field theory. This method uses a UV basis of conformal Casimir eigenstates, which is truncated at some maximum Casimir eigenvalue, to approximate the low energy spectrum of the IR theory. So far, such methods have been limited to theories in 2D, and I will present a new framework for generalizing this approach to higher dimensions.
I will discuss a class of non-compact solutions to the Strominger-Hull system, the first order system of equations for preserving N=1 supersymmetry in heterotic compactifications to four dimensions. The solutions consists of the conifold and its Z2 orbifold with Abelian gauge fields and non-zero three-form flux. The heterotic Bianchi Identity is solved in a large charge limit of the gauge fields, where it is shown that the topological term p1(TX) can be consistently neglected. At large distances, these solutions are locally Ricci-flat.
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.