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##### Dynamics and fields for tensor networks

Tobias Osborne (Leibniz Universität Hannover) Slides

*Abstract:* I describe how take the continuous limit of discrete hierarchical tensor networks, such as tree tensor networks, which may be achieved via the semicontinuous limit of Jones. Dynamics are then introduced by building a unitary representation of a group known as Thompson’s group *T*, which is a discretised analogy of the conformal group $\textrm(\mathbb{R}^{1,1})$. Field operators may be defined for the boundary theory yielding a theory with discrete scaling symmetry.top [^]

##### Compact Hypergroups in Conformal Field Theory

Simone Del Vecchio (Universität Leipzig) Slides

*Abstract:* The question that will be discussed in this talk is: given a chiral conformal net A on the circle, how can we characterize conformal subnets B ⊆ A? An answer will be provided when the local algebras of the conformal embedding give rise to discrete subfactors (namely either finite Jones index or possibly infinite index with some additional regularity assumption), using the notion of compact hypergroup. I will show how to canonically construct a compact hypergroup from data of the subfactor. This hypergroup has a natural action on A and recovers B as the fixed points of its action, thus generalizing orbifolds by compact groups. Additionally it contains information on the representation category of the subfactor. I will then discuss applications of this construction, in particular I will show that when the conformal net A is local then orbifolds by compact quantum groups are ruled out.

Based on joint work with Marcel Bischoff (Ohio University) and Luca Giorgetti (Vanderbilt University). top [^]

##### Equivalence of tensor categories in rational conformal field theories

Bin Gui (Rutgers University) Slides

*Abstract:* The first key step in studying rational CFT is to understand the representation category of the algebras of chiral fields. Such algebras are called (regular/ rational and $C_2$ cofinite) vertex operator algebras in the Euclidean spacetime, or (completely rational) conformal nets in the Minkowski spacetime. Although these two types of chiral algebras are studied in very different ways (due to the difference of spacetimes), one expect that their representation categories are equivalent. In this talk, I will report recent progress in proving such equivalence. top [^]

##### About the correspondence between vertex operator superalgebras and graded-local conformal nets

Tiziano Gaudio (Lancaster University) Slides

*Abstract:* In a paper of 2018, Carpi, Kawahigashi, Longo and Weiner describe the correspondence which subsists between two different formulations of local chiral conformal field theory: the axiomatization via vertex operator algebras and the one via (local) conformal nets. If we are also interested in graded-local models of chiral conformal field theory, then the question about whether and how that correspondence works will arise quite naturally. In this talk, we answer that question, using the notions of vertex operator superalgebra and graded-local conformal net, which are natural extensions of the ones above. Furthermore, we upgrade several results contained in the paper mentioned above to the graded-local case. (Joint work with S. Carpi and R. Hillier.)top [^]

##### A soft-photon theorem for the Maxwell-Lorentz system

Duc Viet Hoang (Ludwig Maximilian University of Munich) Slides

*Abstract:* For the coupled system of classical Maxwell-Lorentz equations I will show that ${\mathfrak{F}}(\hat x, t)=\lim_{|x|\to \infty} |x|^2 F(x,t)$ and $\mathcal{F}(\hat k, t)=\lim_{|k|\to 0} |k| \widehat{F}(k,t)$, where $F$ is the Faraday tensor, $\hat{F}$ its Fourier transform in space and $\hat{x}:=\frac{x}{|x|}$, are independent of $t$. Combined with the scattering theory for the Maxwell-Lorentz system due to Komech and Spohn, this observation gives the asymptotic decoupling of $F$ into the scattered radiation $F_{\mathrm{sc},\pm}$ and the soliton field $F_{v_{\pm\infty}}$ depending on the asymptotic velocity $v_{\pm\infty}$ of the electron at large positive (+), resp. negative (-) times. This yields a *soft-photon theorem* of the form $\mathcal{F}_{\text{sc},+}(\hat{k}) - \mathcal{F}_{\text{sc},-}(\hat{k})= -( \mathcal{F}_{v_{+\infty}}(\hat{k})-\mathcal{F}_{v_{-\infty}}(\hat{k}))$, and analogously for $\mathfrak{F}$, which links the low-frequency part of the scattered radiation to the change of the electron's velocity. Implications for the infrared problem in QED are discussed. This is a joint project with Wojciech Dybalski. top [^]

##### Herdegen’s algebraic approach to Casimir effect. What two plates and two delta like systems tells as about?

Kamil Ziemian (Jagiellonian University in Cracow) Slides

*Abstract:* Herdegen's algebraic approach to Casimir effect provides a framework which allow us to derive rigorous result about systems in which change of quantum ground state cause adiabatic change in state of macroscopic bodies. In first part of the talk, the outline of physical and mathematical basics of this formalism would be given. In the second part, obtained results would be presented: for scalar and electromagnetic field system in two plate settings derived by Herdegen and Stopa, and recently for scalar field in two delta-like systems by the speaker. They strongly suggest that modification of quantum state in vicinity of macroscopic bodies is crucial to understand Casimir effect, but in standard treatment is often removed or obscured by renormalization procedure. top [^]

##### Measurement schemes in local quantum physics

Chris Fewster (University of York) Slides

*Abstract:* A standard account of the measurement chain in quantum mechanics involves a probe (itself a quantum system) coupled temporarily to the system of interest. Once the coupling is removed, the probe is measured and the results are interpreted as the measurement of a system observable. This arrangement forms a measurement scheme for the latter observable. Measurement schemes have been studied extensively in Quantum Measurement Theory, but they are rarely discussed in the context of quantum fields and still less on curved spacetimes. Meanwhile, although algebraic quantum field theory is founded on the idea of local observables, their practical measurement has been left largely unexplored.

In this talk I will describe how measurement schemes may be formulated for quantum fields on curved spacetime within the general setting of algebraic QFT. This allows the discussion of the localisation and properties of the system observable induced by a probe measurement, and the way in which a system state can be updated thereafter. The framework is local and fully covariant, allowing the consistent description of measurements made in spacelike separated regions. Furthermore, specific models can be given in which the framework may be exemplified by concrete calculations.

I will also explain how this framework can shed light on an old problem due to Sorkin concerning "impossible measurements" in which measurement apparently conflicts with causality.

The talk is based on work with Rainer Verch [Leipzig], arXiv:1810.06512 (to appear, Comm. Math. Phys.); see also arXiv:1904.06944 for a summary, and a recent preprint arXiv:2003.04660 with Henning Bostelmann and Maximilian H. Ruep [York]. top [^]

##### Existence and uniqueness of solutions of the semiclassical Einstein equation in cosmological models

Paolo Meda (University of Genoa) Slides

*Abstract:* We discuss the existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In this case, contributions with derivatives of the metric higher than the second appear, also in a non-local form. Preliminarily, we show that a state for the quantum matter compatible with the initial data for the geometry can be always selected. Then, after a partial integration of the semiclassical equations, we identify the non-local contribution with higher derivatives inside the quantum state in form of an unbounded operator applied to a function of the scale factor and its second derivative. First, we show that an inversion formula can be obtained for this operator respecting the causality. Secondly, that formula yields a fixed-point equation when it is applied to the traced semiclassical Einstein equation and hence it can be solved by means of the Banach fixed-point theorem. This analysis reveals that a solution of the semiclassical equation cannot be computed by using the standard methods and suggests that the semiclassical Einstein equation needs to be rewritten in a new non-standard form. Joint work with N. Pinamonti and D. Siemssen. top [^]

##### On the construction of Feynman parametrices for normally hyperbolic operators

Onirban Islam (University of Leeds) Slides

*Abstract:* Feynman parametrices are an essential ingredient of perturbative quantum field theory. They also play a pivotal role in the Bär-Strohmaier Lorentzian index theorem and the Lorentzian generalisation of Duistermaat-Guillemin-Gutzwiller semiclassical trace formula. A classic result by Duistermaat-Hörmander asserts that there exist unique Feynman parametrices on a smooth manifold that is pseudo-convex with respect to a pseudodifferential operator of real-principal type. In this talk, I review the results for normally hyperbolic operator, sketch the basic ideas of Duistermaat and Hörmander’s arguments, and explain to what extent this generalises to vector bundles. (Joint work with A. Strohmaier). top [^]

##### High-energy bounds on Møller operators

Henning Bostelmann (University of York) Slides

*Abstract:* Scattering processes in quantum mechanics are expected to be suppressed at high energies: if $\Omega$ is the Møller operator, one expects that $\Omega \approx 1$ on high spectral subspaces for, say, the free Hamiltonian. We analyze this phenomenon in a general setting of scattering theory, starting from two self-adjoint operators and their associated Møller operators. We formulate a quantitative notion of "high energy bounds" in this context. Then we provide sufficient criteria for these bounds that can be verified in concrete models; among them are the perturbed polyharmonic operator and Schrödinger operators with matrix-valued potentials. Applications include the problem of quantum backflow. top [^]

##### Covariant homogeneous nets of standard subspaces

Vincenzo Morinelli (University of Rome Tor Vergata) Slides

*Abstract:* The Brunetti-Guido-Longo (BGL) construction for the free field relies on the Bisognano-Wichmann (B-W) property and the implementation of a CPT operator in terms of the Tomita modular conjugations. In this way, given an (anti-)unitary positive energy representation of the symmetry group, the one-particle net on wedge regions is uniquely determined and its second quantization corresponds to the free field net. In this talk we will present how this construction can be generalized in the following sense. Given a Lie group G with a 2-grading, it is possible to define at the Lie algebra level an abstract object called wedge. This definition complies with G-covariance and fundamental wedge relative positions as the wedge inclusions (when a positive cone in the lie algebra is defined) and the wedge (spacelike) complement. Note that no spacetime is required for this construction. When the Lie algebra supports wedges it is possible to define an Haag-Kastler net on this set of wedges starting from an (anti-)unitary positive energy representation of the group assuming identifications analogously to (B-W) and the CPT-Tomita conjugations. This generalizes the Haag-Kastler picture, includes the most famous examples and gives perspectives on further possible models in QFT.

This talk is based on an ongoing joint work with K.-H. Neeb (Univ. Nürnberg-Erlangen). top [^]

##### Spin_{c} spectral geometry and fermion doubling

Arkadiusz Bochniak (Jagiellonian University) Slides

*Abstract:* Despite tremendous success the formulation of the Standard Model in the language of noncommutative geometry still suffers from few problems. Most significantly, it is Euclidean and leads to the quadrupling of the degrees of freedom. We propose a simple model of the noncommutative spin_{c} geometry, for which there is no fermion doubling, it does not lead to the possibility of color symmetry breaking and can also explain the origin of the CP violation. top [^]

##### A new construction of strict deformation quantization for Lagrangian fiber bundles

Mayuko Yamashita (Kyoto University) Slides

*Abstract:* In this talk, I will explain a new construction of strict deformation quantization for Lagrangian fiber bundles. This construction can be regarded as a "lattice approximation" of the correspondence between differential operators and principal symbols. As an application, I will also explain an ongoing joint work with Yosuke Kubota, to develop a lattice version of Atiyah-Singer index theorem and its application to the index problem of Wilson-Dirac operators. top [^]

##### Private Capacity and Subfactors

Carolina Dias Alexiou (Tokyo University) Slides

*Abstract:* Private Capacity of wiretap channels gives a way to measure the amount of information that can be kept secret between a sender and receiver. It is known that such capacity is not additive, but it motivates the question: for which class of channels is the private capacity additive? Although this quantity has alternative formulations in finite dimensional systems, it is not clear that those would also work on a general von Neumann algebra setting. Recent works show that one could obtain full additivity if these formulations were to be naively extended. In parallel, the study of private quantum channels gave birth to the theory of Private Quantum Subsystems, which is naturally more compatible with subfactors. In this talk I will discuss both approaches and general ideas. This work is currently in progress and it is part of my PhD. top [^]

##### Entropy in Causal Fermion Systems (ideas, current state of research)

Magdalena Lottner (Universität Regensburg) Slides

*Abstract:* The Theory of Causal Fermion Systems is a novel approach to fundamental physics. It provides a unification of the interactions of the standard model with gravity on the level of classical field theory. Moreover, it gives close connections to quantum field theory.

A recent topic of interest is how one can define entropy in this theory. I will present a proposal for a general definition of an entanglement entropy. It is formulated in terms of surface layer integrals which generalize two- and three-dimensional surface integrals to the setting of causal fermion systems. This entanglement entropy can be written as a series of nested surface layer integrals. First calculations for the lowest order surface layer integral show that the leading contribution to the entropy scales like the area. This gives hope to find a relation between entanglement entropy and the area law, which could be used to address the black hole information paradox in the Theory of Causal Fermion Systems.

In my talk I will give a brief overview of the general ideas and the current state of research on this topic. This is work in progress as part of my PhD thesis in the group of Felix Finster. top [^]

##### Entropy and split inclusions in AdS/CFT

Thomas Faulkner (UIUC)

*Abstract:* Entanglement Entropies in AdS/CFT, studied via the Ryu Takayanagi formula, are an important tool for studying the emergence of gravity from QFT. Unfortunately, from an algebraic approach to the subject, it is not clear how to best define/regulate these entropies in the continuum. The split property gives one such possible regulator, via the von Neumann entropy of a type-I factor. I will discuss a conjecture for the AdS/CFT dictionary that computes this quantity. top [^]

##### Towards a manifestly supersymmetric formulation of Loop quantum supergravity

Konstantin Eder (FAU Erlangen-Nürnberg) Slides

*Abstract:* We study the idea to quantize supergravity in the framework of loop quantum gravity in a way such that the resulting theory still reflects, at least partially, the underlying supersymmetry. Therefore, following the approach of D'Aurea and Fre, we consider supergravity as super Cartan geometry and derive a super analog of Ashtekar's connection. This sets the stage for a quantisation of the theory that might lead to a unified description of both, gravity and matter degrees of freedom. top [^]

##### Strong cosmic censorship and quantum fields

Jochen Zahn (Universität Leipzig) Slides

*Abstract:* In recent years it has been established that (the Christodoulou formulation of) strong cosmic censorship is violated in near extremal Reissner-Nordström-deSitter black holes: The divergence of perturbations at the Cauchy horizon becomes weak enough, allowing for a non-unique extension (as a weak solution) beyond the Cauchy horizon, thus undermining determinism. We show that for quantum fields, the degree of divergence of the expectation value of the stress tensor near the Cauchy horizon is state-independent, universal, and strong enough to save strong cosmic censorship. Joint work with Stefan Hollands and Bob Wald. top [^]