KZ connections with irregular singularities have monodromies that realize topological invariants of links and tangles.
A Long Exact Sequence in Symmetry Breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases
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abstract
We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations which sometimes occur at the cores of these objects. These are topologically protected by an 't Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects, and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories, which we call the "symmetry breaking long exact sequence" (SBLES). The mathematical backbone of the SBLES is studied in a companion paper. Our work further develops the theory of higher Berry phase and its bulk-boundary correspondence, and serves as a new computational tool for classifying symmetry protected topological phases.
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Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.
Diabolical critical points are stable higher-codimension defects in parameter space of quantum and classical many-body systems, defined by non-trivial winding of nearby equilibrium states.
citing papers explorer
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On the monodromy of KZ-connections with irregular singularities
KZ connections with irregular singularities have monodromies that realize topological invariants of links and tangles.
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Generalized Families of QFTs
Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.
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In search of diabolical critical points
Diabolical critical points are stable higher-codimension defects in parameter space of quantum and classical many-body systems, defined by non-trivial winding of nearby equilibrium states.
- When Symmetries Twist: Anomaly Inflow on Monodromy Defects