AQFTUK

5 & 6 June 2025 at Cardiff University

Location: Abacws/3.38

We are pleased to announce the 10th  workshop of the AQFT in the UK research network. We have a limited amount of financial support available for participants that do not have any other sources of funding. Please get in touch with the organisers (Naomi Wray wraynj@cardiff.ac.uk and Pieter Naaijkens naaijkensp@cardiff.ac.uk) if this would be of use to you.

Schedule

We will start on Thursday at 13:30. On Friday, the last talk finishes around 16:00. This should give enough time for most UK participants to arrive on Thursday and leave on Friday.

Abstracts

Tomasz Maciazek
(University of Bristol)

Title:  Anyon braiding on 1D quantum wire networks from first principles

Abstract:  World lines of particles that exchange in 2D form braids in spacetime. These braids are subject to certain universal topological relations coming from their continuous deformations (homotopy). In 2D such an approach leads to the well-known braiding relation also known as the Yang-Baxter relation. In my talk I will show how to define counterparts of braids and derive braiding relations for particles constrained to move on planar wire networks. I will demonstrate that particles on wire networks have fundamentally different braiding properties than particles in 2D. My analysis reveals an unexpectedly wide variety of possible non-abelian braiding behaviours on networks. The character of braiding depends on the topological invariant called the connectedness of the network. As one of our most striking consequences, particles on modular networks can change their statistical properties when moving between different modules. However, sufficiently highly connected networks already reproduce braiding properties of 2D systems.

In the second part of my talk, I will analyse the ways of realising the braiding of anyons on networks in a topological quantum field theory setting where anyons are allowed to braid as well as fuse. The compatibility of fusion and braiding on networks leads to new types of hexagon equations which in turn allow more general braid actions than the ones which are known from 2D physics.

James MacManus
(University of Nottingham)

Title: An Equivalence Theorem for Algebraic and Functorial QFT

Abstract: In this talk I will discuss the relationship between two prominent approaches to the axiomatisation of quantum field theory, namely algebraic quantum field theories (AQFT) and functorial field theories (FQFT). In particular, I will present an equivalence theorem between AQFTs and globally hyperbolic Lorentzian FQFTs, both subject to the time-slice axiom and additivity conditions. The key issue faced here is in designing a concept of bordism which is rich enough to capture the spatially local features one recognises in algebraic QFT, without altering the topology of the Cauchy surfaces. This is addressed by generalising the geometric bordism pseudo-categories of Stolz and Teichner to a Lorentzian bordism pseudo-operad which presents bordisms as morphisms from tuples of causally disjoint partial Cauchy surfaces to a full Cauchy surface. This allows us to meaningfully define a category of globally hyperbolic Lorentzian FQFTs and compare this with the category of AQFTs through quasi-inverse functors.

This talk is based on joint work with Severin Bunk and Alexander Schenkel [2504.15759].

Daan Janssen
(University of York)

Title: Semi-local observables in electromagnetism, edge modes and Hadamard states

Abstract: We consider an algebra of semi-local observables for the quantum electromagnetic field on spacetimes with corners, including observables sensitive to large gauge degrees of freedom or edge modes. We show that these edge mode observables define an operational quantum reference frame associated with large gauge transformations, and discuss how these frames can be used in gluing procedures of algebras and quantum states. Furthermore, we show that this algebra of semi-local observables admits physically well-behaved (Hadamard) states and representations, for which we discuss their decomposition into superselection sectors of the algebra of local observables.

Mike Blake
(University of Bristol)

Title: The Page curve from the entanglement membrane

Abstract: We study entanglement dynamics in toy models of black hole information built out of chaotic many-body quantum systems, by utilising a coarse-grained description of entanglement dynamics in such systems known as the `entanglement membrane'. We show that in these models the Page curve associated to the entropy of Hawking radiation arises from a transition in the entanglement membrane around the Page time, in an analogous manner to the change in quantum extremal surfaces that leads to the Page curve in semi-classical gravity. We also use the entanglement membrane prescription to study the Hayden-Preskill protocol, and demonstrate how information initially encoded in the black hole is rapidly transferred to the radiation around the Page time. Our results relate recent developments in black hole information to generic features of entanglement dynamics in chaotic many-body quantum systems. Based on work with Anthony Thompson. 

Kasia Rejzner
(University of York)

Title: Hidden boundaries in perturbative AQFT

Abstract: Perturbative AQFT is a rigorous framework combining aspects of local quantum physics with perturbative methods. Construction of models involves using generalized Lagrangians which are maps from the space of test functions to local functionals. The idea is that the test function introduces the adiabatic cutoff for the Lagrangian density and hence one avoids the IR problem. I will argue that using such a test function can be seen as working in a relatively compact region with a smoothened boundary and that some of the standard methods of the BV-BFV formalism could be applied. 

This talk is based on a joint work with Michele Schiavina.

Alexander Schenkel
(University of Nottingham)

Title: Haag-Kastler stacks

Abstract: I will present an overview of the recently introduced concepts of Haag-Kastler 2-functors and Haag-Kastler stacks, which offer a novel and flexible framework for organizing the data of algebraic quantum field theories (AQFTs) defined across all globally hyperbolic spacetimes. A key feature of this framework is the existence of decomposition and assembly functors that connect locally covariant AQFTs to points of the Haag-Kastler 2-functor. These constructions enable the decomposition of difficult global problems on the category of spacetimes Loc into families of simpler local problems on individual spacetimes. As a concrete application, I will demonstrate how these tools simplify the global infinity-categorical equivalence problem between AQFTs and prefactorization algebras into a family of simpler local equivalence problems. Finally, I will illustrate how the perspective of Haag-Kastler stacks introduces new descent conditions (i.e. local-to-global properties), which allow the reconstruction of an AQFT on a spacetime M from a compatible family of AQFTs defined on a causally convex open cover $\{U_i \subseteq M\}$.

This talk is based on joint work with Benini and Grant-Stuart [2404.14510] and Benini, Carmona and Grant-Stuart [2412.07318].

Gandalf Lechner
(FAU Erlangen)

Title: On causal and covariant space(time) localisation observables

Abstract: In this talk I shall consider the problem of finding localisation observables that are compatible with the basic structures of quantum physics, formulated in terms of the logic of quantum mechanics and causality / covariance requirements. After reviewing well-known no-go theorems, it will be shown that a modification of the logic of quantum mechanics (governed by complex orthogonal projections) to a quasi-logic governed by real orthogonal projections, the obstructions disappear and the resulting structure can be naturally represented in terms of modular theory. I will also discuss to which extent this construction yields localisation properties by considering their cluster properties.

This talk is based on joint work with Ivan Romualdo de Oliveira. 

Ian Koot
(FAU Erlangen)

Title: Relative Positions of Half-sided Modular Inclusions

Abstract:  Tomita-Takesaki modular theory has become a powerful tool in the analysis of quantum field theories. Although generally the modular objects are difficult to calculate explicitly, in the setting of Half-sided Modular Inlcusions we have more control over them. These inclusions are not just mathematically easier, but are also of physical interest, as they arise naturally in vacuum theories and thermal theories. I will discuss these inclusions in the setting of Standard Subspaces (which are natural from the perspective of modular theory) as well as a recent result which allows one to reduce questions about inclusions of Standard Subspaces in this context to inclusions of associated complex subspaces.

Naomi Wray
(Cardiff University)

Title: Stacking quantum spin systems and the triviality of invertible phases

Abstract: Kitaev introduced the idea of invertible phases, grouping them with states of short-range entanglement. Further, he argued that gapped systems with invertible ground states cannot host anyonic excitations. In this talk, I will present the results of collaborative research in which we have shown this argument within the context of Naaijkens' superselection sectors. Further to this, the string-like automorphisms localised in a chosen cone form a braided tensor C*-category with intertwiners as arrows. Our additional results demonstrate that the category for automorphisms of stacked systems is a categorical tensor product of the categories for each layer. 

This talk is based on joint work with Pieter Naaijkens, Sven Bachmann, and Alan Getz.