Some comments on 6d global gauge anomalies

Abstract

Global gauge anomalies in $6d$ associated with non-trivial homotopy groups ${\pi }_6(G)$ for $G=SU(2)$, $SU(3)$, and $G_2$ were computed and utilized in the past. In the modern bordism point of view of anomalies, however, they come from the bordism groups ${\Omega }_7^{\text{spin}}(BG)$, which are in fact trivial and therefore preclude their existence. Instead, it was noticed that a proper treatment of the $6d$ Green-Schwarz mechanism reproduces the same anomaly cancellation conditions derived from ${\pi }_6(G)$. In this paper, we revisit and clarify the relation between these two different approaches.

arXiv comment35 pages; v2: minor changes and additional references, version to be published

References in corpus (17)

• On Flux Quantization In M-Theory And The Effective Action
• D-Brane Instantons and K-Theory Charges
• Anomaly polynomial of general 6d SCFTs
• Dai-Freed anomalies in particle physics
• Global aspects of the space of 6D N = 1 supergravities
• Holographic Action for the Self-Dual Field
• Classification of abelian spin Chern-Simons theories
• Global Anomalies and Geometric Engineering of Critical Theories in Six Dimensions
• More anomaly-free models of six-dimensional gauged supergravity
• Quadratic functions in geometry, topology,and M-theory
• The global anomaly of the self-dual field in general backgrounds
• Anomaly inflow and $p$-form gauge theories
• Geometric quantization and the metric dependence of the self-dual field theory
• Relative quantum field theory
• The anomaly line bundle of the self-dual field theory
• Canonical quadratic refinements of cohomological pairings from functorial lifts of the Wu class
• A Brief Summary Of Global Anomaly Cancellation In Six-Dimensional Supergravity

Cited by in corpus (2)

• Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
• Cancelling mod-2 anomalies by Green-Schwarz mechanism with $B_{\mu \nu }$