The Fate of Discrete 1-Form Symmetries in 6d

Abstract

Recently introduced generalized global symmetries have been useful in order to understand non-perturbative aspects of quantum field theories in four and lower dimensions. In this paper we focus on 1-form symmetries of weakly coupled 6d supersymmetric gauge theories coupled to dynamical tensor multiplets. We study the consistency of global 1-form symmetries corresponding to the center of the gauge groups, or subgroups thereof, by activating their background fields, which makes the instanton density fractional. In 6d, an instanton background for a given gauge theory sources BPS strings via tadpole cancellation. The non-trivial 1-form symmetry background configurations contribute to the charge of the BPS strings. However, Dirac quantization imposes restrictions on the consistent 1-form backgrounds, since they can in general lead to and induce fractional charges, thus making (part of) the putative higher-form symmetry inconsistent. This gives explicit criteria to determine whether the discrete 1-form symmetries are realized. We implement these criteria in concrete examples originating from string compactifications. We also corroborate this by finding that a non-trivial fractional contribution is related to states which explicitly break the global 1-form symmetry appearing as massive excitations of the 6d BPS strings. For 6d theories consistently coupled to gravity, this hints at a symmetry breaking tower of states. When the fractional contributions are absent, the F-theory realization of the theories points to the gauging of the 1-form symmetry via the presence of non-trivial Mordell--Weil torsion.

48 pages + appendices, 1 figure; v3: typos correct, improved discussion, published version

References in corpus (19)

• Generalized Global Symmetries
• On the Geometry of the String Landscape and the Swampland
• Symmetries and Strings in Field Theory and Gravity
• The Swampland: Introduction and Review
• 6d Conformal Matter
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• Anomaly polynomial of general 6d SCFTs
• The Uncertainty of Fluxes
• Heisenberg Groups and Noncommutative Fluxes
• Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
• 2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• String Universality and Non-Simply-Connected Gauge Groups in 8d
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• TASI 2003 Lectures on Anomalies
• Lectures on Anomalies
• Higher Form Symmetries of Argyres-Douglas Theories
• Instantons, Symmetries and Anomalies in Five Dimensions
• E + E $\to$ H

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• Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
• 2-Group Symmetries of 6d Little String Theories and T-duality
• On the Swampland Cobordism Conjecture and Non-Abelian Duality Groups
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• Charge completeness and the massless charge lattice in F-theory models of supergravity