Quantization of anomaly coefficients in 6D $\mathcal{N}=(1,0)$ supergravity

Abstract

We obtain new constraints on the anomaly coefficients of 6D $\mathcal{N}=(1,0)$ supergravity theories using local and global anomaly cancellation conditions. We show how these constraints can be strengthened if we assume that the theory is well-defined on any spin space-time with an arbitrary gauge bundle. We distinguish the constraints depending on the gauge algebra only from those depending on the global structure of the gauge group. Our main constraint states that the coefficients of the anomaly polynomial for the gauge group $G$ should be an element of $2H^4(BG;\mathbb{Z})\otimes {\Lambda }_S$ where ${\Lambda }_S$ is the unimodular string charge lattice. We show that the constraints in their strongest form are realized in F-theory compactifications. In the process, we identify the cocharacter lattice, which determines the global structure of the gauge group, within the homology lattice of the compactification manifold.

42 pages. v3: Some clarifications, typos corrected

References in corpus (6)

• On the Geometry of the String Landscape and the Swampland
• Symmetries and Strings in Field Theory and Gravity
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• Global aspects of the space of 6D N = 1 supergravities
• Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
• Exotic matter on singular divisors in F-theory

Cited by in corpus (32)

• Dai-Freed anomalies in particle physics
• Cobordism Conjecture, Anomalies, and the String Lamppost Principle
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Anomaly of the Electromagnetic Duality of Maxwell Theory
• Curvature squared invariants in six-dimensional $\mathcal{N}=(1,0)$ supergravity
• Generic matter representations in 6D supergravity theories
• String Defects, Supersymmetry and the Swampland
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• Non-Simply-Connected Symmetries in 6D SCFTs
• Large U(1) charges in F-theory
• Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
• Abelian F-theory Models with Charge-3 and Charge-4 Matter
• A Modern Point of View on Anomalies
• The Geometry of the SU(2)$\times$ G${}_2$-model
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Anomaly inflow and $p$-form gauge theories
• The Green-Schwarz Mechanism and Geometric Anomaly Relations in 2d (0,2) F-theory Vacua
• Charge completeness and the massless charge lattice in F-theory models of supergravity
• Global tensor-matter transitions in F-theory
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• An infinite swampland of U(1) charge spectra in 6D supergravity theories
• Towards a complete classification of 6D supergravities
• Automatic Enhancement in 6D Supergravity and F-theory Models
• The Fate of Discrete 1-Form Symmetries in 6d
• Flavor Symmetries and Automatic Enhancement in the 6d Supergravity Swampland
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Dyonic Black Strings and the Charge Lattice in Salam-Sezgin model
• Orders of Vanishing and U(1) Charges in F-theory
• On the consistency of a class of R-symmetry gauged 6D N=(1,0) supergravities
• Cancelling mod-2 anomalies by Green-Schwarz mechanism with $B_{\mu \nu }$
• A Brief Summary Of Global Anomaly Cancellation In Six-Dimensional Supergravity