Derives the symmetry breaking long exact sequence relating defect anomalies to broken symmetry anomalies, with applications to higher Berry phases and obstructions to local defects in symmetry breaking phases.
18, 26 [Xio18] Charles Zhaoxi Xiong
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A bordism computation for K(Z,3) produces two new anomaly classes for U(1) 1-form symmetries: a mixed H₃∧p₁ anomaly in 5d and a Z₂-valued uSq²u anomaly in 7d.
Family unification models from E7 cosets have no global sigma model anomalies because the torsion parts of their bordism groups vanish, as computed via the Atiyah-Hirzebruch spectral sequence, including when isotropy subgroups are gauged.
Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.
Smith homomorphisms are defined equivalently via Thom spectrum maps, yielding a fiber sequence whose Anderson dual produces long exact sequences of invertible field theories.
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
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A Long Exact Sequence in Symmetry Breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases
Derives the symmetry breaking long exact sequence relating defect anomalies to broken symmetry anomalies, with applications to higher Berry phases and obstructions to local defects in symmetry breaking phases.
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On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies
A bordism computation for K(Z,3) produces two new anomaly classes for U(1) 1-form symmetries: a mixed H₃∧p₁ anomaly in 5d and a Z₂-valued uSq²u anomaly in 7d.
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Anomalies in family unification models from bordism classification
Family unification models from E7 cosets have no global sigma model anomalies because the torsion parts of their bordism groups vanish, as computed via the Atiyah-Hirzebruch spectral sequence, including when isotropy subgroups are gauged.
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Morse-Bott inequalities, Topology Change and Cobordisms to Nothing
Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.
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The Smith Fiber Sequence and Invertible Field Theories
Smith homomorphisms are defined equivalently via Thom spectrum maps, yielding a fiber sequence whose Anderson dual produces long exact sequences of invertible field theories.
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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.