The algebra of anomaly interplay

Abstract

We give a general description of the interplay that can occur between local and global anomalies, in terms of (co)bordism. Mathematically, such an interplay is encoded in the non-canonical splitting of short exact sequences known to classify invertible field theories. We study various examples of the phenomenon in 2, 4, and 6 dimensions. We also describe how this understanding of anomaly interplay provides a rigorous bordism-based version of an old method for calculating global anomalies (starting from local anomalies in a related theory) due to Elitzur and Nair.

arXiv comment55 pages, 10 figures. Added figure illustrating the construction of a nullbordism for the U(2) mapping torus; added explicit computations of the generators of various groups classifying local anomalies (for all 4d examples), together with the 6d bordism generators to which they are dual; other minor corrections and added references

References in corpus (24)

• Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics
• The effects of interactions on the topological classification of free fermion systems
• Fermion Path Integrals And Topological Phases
• Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces
• Anomalies, Dualities, and Topology of D=6 N=1 Superstring Vacua
• Interacting topological phases and modular invariance
• The "Parity" Anomaly On An Unorientable Manifold
• Eta-Invariants and Determinant Lines
• Dai-Freed anomalies in particle physics
• A New SU(2) Anomaly
• Higher Anomalies, Higher Symmetries, and Cobordisms I: Classification of Higher-Symmetry-Protected Topological States and Their Boundary Fermionic/Bosonic Anomalies via a Generalized Cobordism Theory
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Why are fractional charges of orientifolds compatible with Dirac quantization?
• Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
• Dai-Freed theorem and topological phases of matter
• Global anomalies in the Standard Model(s) and Beyond
• 8d gauge anomalies and the topological Green-Schwarz mechanism
• Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism
• Remarks on the Green-Schwarz terms of six-dimensional supergravity theories
• Topological Superconductors on Superstring Worldsheets
• Revisiting Wess-Zumino-Witten terms
• GSO projections via SPT phases
• Anomaly interplay in $U(2)$ gauge theories
• Hamiltonian anomalies from extended field theories

Cited by in corpus (21)

• Global Anomalies on the Hilbert Space
• Anomalies and Symmetry Fractionalization
• The anomaly that was not meant IIB
• Electroweak flavour unification
• Anomalies and gauging of U(1) symmetries
• Topological modular forms and the absence of all heterotic global anomalies
• Omega vs. pi, and 6d anomaly cancellation
• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Anomalies of non-Abelian finite groups via cobordism
• Spin-cobordisms, surgeries and fermionic modular bootstrap
• Toric 2-group anomalies via cobordism
• Fractionally Charged Particles at the Energy Frontier: The SM Gauge Group and One-Form Global Symmetry
• Atiyah-Patodi-Singer index theorem from axial anomaly
• On a ${\mathbb{Z}}_3$-valued discrete topological term in 10d heterotic string theories
• What bordism-theoretic anomaly cancellation can do for U
• A Long Exact Sequence in Symmetry Breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases
• The Smith Fiber Sequence and Invertible Field Theories
• Comments on the Atiyah-Patodi-Singer index theorem, domain wall, and Berry phase
• Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders
• Smith homomorphisms and Spin${}^h$ structures
• Cancelling mod-2 anomalies by Green-Schwarz mechanism with $B_{\mu \nu }$