The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings

Abstract

We study global anomalies of discrete gauge symmetries in six-dimensional supergravities and their realizations in F-theory. We explicitly construct a discrete Green-Schwarz mechanism that depends on the choice of a coupling constant and on a certain quadratic refinement in differential cohomology. By geometrically engineering theories with $G={\mathbb{Z}}_3$ gauge symmetry and no tensor multiplets, we observe that a particular choice of the quadratic refinement is singled out in F-theory. This implies new Swampland constraints on the discrete charge spectra of 6d supergravities. On the other hand, the discrete Green-Schwarz coupling depends on the geometry of the Calabi-Yau. We use anomaly inflow to relate this to a 't Hooft anomaly of the induced global symmetry in the worldsheet theories of non-critical strings. Using topological symmetry lines, we further relate this anomaly to the modular properties of twisted-twined elliptic genera. We then argue that the latter are encoded in the A-model topological string partition functions on different torus fibrations that are equipped with a flat torsional B-field. This allows us to derive a geometric expression for the global discrete anomaly in terms of the height-pairing of a multi-section on a genus one fibered Calabi-Yau.

35+16 pages, 21 figures

References in corpus (21)

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• The Swampland: Introduction and Review
• Lectures on the Swampland Program in String Compactifications
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
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• Yukawas and discrete symmetries in F-theory compactifications without section
• Dai-Freed theorem and topological phases of matter
• Anomaly of strings of 6d $\mathcal{N}=(1,0)$ theories
• 8d gauge anomalies and the topological Green-Schwarz mechanism
• The anomaly that was not meant IIB
• Global anomalies in 8d supergravity
• The algebra of anomaly interplay
• Anomaly interplay in $U(2)$ gauge theories
• Omega vs. pi, and 6d anomaly cancellation
• Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
• Anomalies of non-Abelian finite groups via cobordism
• Modularity from Monodromy

Cited by in corpus (3)

• Bordism for the 2-group symmetries of the heterotic and CHL strings
• Topological Strings on Non-Commutative Resolutions
• Cancelling mod-2 anomalies by Green-Schwarz mechanism with $B_{\mu \nu }$