# AQFTUK

## Meeting 20th February 2020

### 20th February 2020 at Lancaster University

(Department of Mathematics and Statistics, PSC Lecture Theatre)

For further information please contact Robin Hillier

The meeting is open to everybody. No registration required.

11:30-12:30 Talk by Pieter Naaijkens (Cardiff): *Stability of anyonic superselection sectors*

12:30-13:45 Lunch

13:45-14:15 Talk by Simen Bruinsma (Nottingham): *Homotopical linear quantum Yang-Mills*

14:20-14:50 Talk by Samuel Crawford (York):* 2D CFT a la pAQFT*

15:00-16:00 Talk by Sebastiano Carpi (Rome Tor Vergata): *Unitary positive energy representations of the W_3 algebra with central charge above two*

16:00-17:00 Coffee and informal discussions

## Abstracts

### Pieter Naaijkens

Consider a continuous path of gapped local Hamiltonians of a quantum spin systems. Two states are said to be in the same quantum phase if they can be realised as the ground state of Hamiltonians connected by such a path. Using techniques first developed in Algebraic Quantum Field Theory by Doplicher, Haag and Roberts, one can find the sector theory of such a given ground state. This tells us what charged excitations (anyons) such states support and what their properties are. These can be described by a (usually modular) braided tensor category. In this talk I will outline how one can show that for topologically ordered states, this whole structure is an invariant of the phase. This means that given any other state in the phase would lead to the same tensor category. Based on joint work with Matthew Cha and Bruno Nachtergaele.

### Simen Bruinsma

We will give a brief explanation of higher categorical structures in gauge theory, and discuss the simplest case, linear gauge theory, which can be modelled by a chain complex. We study the derived critical locus of the linear Yang-Mills action and find that on globally hyperbolic spacetimes this complex allows for trivializations, which are chain complex analogues of (advanced and retarded) Green's operators. These trivializations give rise to an unshifted Poisson structure which is central to quantizing the theory. They also play a central role in relative Cauchy evolution, where new challenges arise when considering chain complexes. This is based on joint work with M. Benini and A. Schenkel [arXiv:1906.00999] and ongoing work with C. Fewster and A. Schenkel.

### Samuel Crawford

Conformal Field Theories in 2 dimensions and with Euclidean signature have been developed rigorously, in particular through the use of Vertex Operator Algebras. During this development, many concepts have arisen which do not have obvious analogues in other mathematically rigorous constructions of QFT. In this talk, I will explain how the fundamentally Lorentzian framework of pAQFT can naturally reproduce the concepts of conformal weights and primary fields. Using the free scalar boson as our model, we will recover the well-known transformation properties of observables such as the (differentiated) field strength and the stress-energy tensor. In doing so we shall see the pAQFT framework may provide a new approach to relating VOAs to AQFT, to complement the already successful study via conformal nets.

### Sebastiano Carpi

The W_3 algebra is an extension of the Virasoro algebra and naturally appears in chiral conformal field theory. I will explain recent results of unitarity of a class of irreducible positive energy representations with central charge above two including the vacuum representations. (Based on a joint work with Yoh Tanimoto and MihĂˇly Weiner)

## How to reach the venue

Some general info https://www.lancaster.ac.uk/about-us/maps-and-travel/#

The talks will take place at the "Postgraduate Statistics Centre" (PSC) indicated on the map below.