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.  This proposal relies on a conjecture about the behavior of entanglement entropies for small spheres.  The calculations presented here suggest that this conjecture must be modified, but I will discuss how Jacobson's derivation still applies under the modified conjecture.  

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.

We studied a holographic superconductor model with a momentum relaxation by employing a linear massless scalar field, which is expected to play a role of impurity via holographic correspondence. By fixing a ratio of impurity/chemical potential, we observed the complex scalar field condensation depending on temperature and computed an electric, thermoelectric, and thermal conductivities. Interestingly, in the presence of the linear massless scalar field, Drude behaviour was shown near a zero frequency regime and the numerical data for the conductivities satisfied Ferrell-Glover-Tinkham (FGT) sum rule. We also numerically checked that the holographic Ward Identity is hold and tried to find if universal law such as Homes law or Uemura’s law is present in our model. However, Homes law was not discovered and Uemera’s law was seen when the charge of the scalar field is 3 and the ratio of the impurity/chemical potential is smaller than about 1/2. 

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.

We construct a new model of four-dimensional relativistic strings with integrable dynamics on the worldsheet. In addition to translational modes this model contains a single massless pseudoscalar worldsheet field - the worldsheet axion. The axion couples to a topological density which counts the self-intersection number of a string. The corresponding coupling is fixed by integrability to Q=716π−−−√≈0.37. We argue that this model is a member of a larger family of relativistic non-critical integrable string models. This family includes and extends conventional non-critical strings described by the linear dilaton CFT. Intriguingly, recent lattice data in SU(3) and SU(5) gluodynamics reveals the presence of a massive pseudoscalar axion on the worldsheet of confining flux tubes. The value of the corresponding coupling, as determined from the lattice data, is equal to QL≈0.38±0.04.