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.

arXiv comment35+16 pages, 21 figures

References in corpus (71)

• Generalized Global Symmetries
• Evidence for F-Theory
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• The Swampland: Introduction and Review
• Compactifications of F-Theory on Calabi--Yau Threefolds -- I
• Geometric Singularities and Enhanced Gauge Symmetries
• A Note on the Green - Schwarz Mechanism in Open - String Theories
• Fermion Path Integrals And Topological Phases
• Five-Brane Effective Action In M-Theory
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• Mirror Symmetry for Two Parameter Models -- II
• Lectures on the Swampland Program in String Compactifications
• On finite symmetries and their gauging in two dimensions
• Tensionless Strings and the Weak Gravity Conjecture
• Reflection positivity and invertible topological phases
• M-Strings
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• BPS States of Exceptional Non-Critical Strings
• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• A Stringy Test of the Scalar Weak Gravity Conjecture
• Dai-Freed anomalies in particle physics
• Low-Energy Analysis of $M$ and $F$ Theories on Calabi-Yau Threefolds
• Global aspects of the space of 6D N = 1 supergravities
• The N=1 effective action of F-theory compactifications
• Anomaly Equations and Intersection Theory
• Generalized Green-Schwarz mechanism in F theory
• Heisenberg Groups and Noncommutative Fluxes
• Twisted differential String and Fivebrane structures
• Physics of F-theory compactifications without section
• Strings of Minimal 6d SCFTs
• Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds
• Mapping 6D N = 1 supergravities to F-theory
• Monad Bundles in Heterotic String Compactifications
• Universal Bounds on Charged States in 2d CFT and 3d Gravity
• F-theory on Genus-One Fibrations
• Discrete Gauge Symmetries by Higgsing in four-dimensional F-Theory Compactifications
• F-Theory, Spinning Black Holes and Multi-string Branches
• Yukawas and discrete symmetries in F-theory compactifications without section
• F-Theory Vacua with Z_3 Gauge Symmetry
• Constraints on 6D Supergravity Theories with Abelian Gauge Symmetry
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Terminal Singularities, Milnor Numbers, and Matter in F-theory
• Gauge Fluxes in F-theory and Type IIB Orientifolds
• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
• Dai-Freed theorem and topological phases of matter
• Quantization of anomaly coefficients in 6D $\mathcal{N}=(1,0)$ supergravity
• Anomaly of strings of 6d $\mathcal{N}=(1,0)$ theories
• Global anomalies in the Standard Model(s) and Beyond
• 8d gauge anomalies and the topological Green-Schwarz mechanism
• On Exceptional Instanton Strings
• Chiral 2d Theories from N=4 SYM with Varying Coupling
• The anomaly that was not meant IIB
• Remarks on the Green-Schwarz terms of six-dimensional supergravity theories
• Fluxes in F-theory Compactifications on Genus-One Fibrations
• F-theory on Quotient Threefolds with (2,0) Discrete Superconformal Matter
• Mixed global anomalies and boundary conformal field theories
• Global anomalies in 8d supergravity
• The algebra of anomaly interplay
• Discrete Gauge Groups in F-theory Models on Genus-One Fibered Calabi-Yau 4-folds without Section
• Mordell-Weil Torsion in the Mirror of Multi-Sections
• Anomaly interplay in $U(2)$ gauge theories
• Omega vs. pi, and 6d anomaly cancellation
• Large U(1) charges in F-theory
• A Modern Point of View on Anomalies
• F-Theory on Quotients of Elliptic Calabi-Yau Threefolds
• High electric charges in M-theory from quiver varieties
• Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
• Modular Curves and Mordell-Weil Torsion in F-theory
• Anomalies of non-Abelian finite groups via cobordism
• The Green-Schwarz Mechanism and Geometric Anomaly Relations in 2d (0,2) F-theory Vacua
• Modularity from Monodromy

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