Erlangen 2026 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quantum Field Theory I: Axiomatic, Probabilistic, Algebraic, Conformal

MP 3.3: Hauptvortrag

Dienstag, 17. März 2026, 17:15–17:45, KH 02.013

Local topological order and boundary algebras — Corey Jones¹, •Pieter Naaijkens², David Penneys³, and Daniel Wallick³ — ¹North Carolina State University, Raleigh, NC, USA — ²Cardiff University, Cardiff, UK — ³The Ohio State University, Columbus, OH, USA

Topologically ordered phases of matter have interesting features, such as the existence of quasi-particles with braid statistics. These quasi-particles can be studied using an AQFT-inspired approach along the lines of the celebrated Doplicher-Haag-Roberts programme on superselection sectors. In this talk I will introduce an axiomatisation, called local topological order, of such quantum models. These axioms are defined in terms of nets of (ground state) projections satisfying certain conditions. They allow us to define a physical boundary algebra, and I will outline how in concrete models (such as Kitaev’s toric code or Levin-Wen models) the bulk superselection sector (“DHR”) category can be recovered from the boundary algebra, giving a mathematical framework for topological holography. If time permits, I will explain how these axioms can be extended to included models with topological boundaries, and outline how this can be used to study, for example, Walker-Wang bulk-boundary systems.

Keywords: topological order; bulk-boundary correspondence; superselection sectors; topological holography; quantum spin systems