Topological Terms and Phases of Sigma Models

2017/10/06 by Ryan Thorngren, Thorngren, Ryan
Computer Science · Mathematics · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Strongly Correlated Electrons (cond-mat.str-el) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1710.02545

openalex publication_date 2017/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study boundary conditions of topological sigma models with the goal of generalizing the concepts of anomalous symmetry and symmetry protected topological order. We find a version of 't Hooft's anomaly matching conditions on the renormalization group flow of boundaries of invertible topological sigma models and discuss several examples of anomalous boundary theories. We also comment on bulk topological transitions in dynamical sigma models and argue that one can, with care, use topological data to draw sigma model phase diagrams.

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