Anomaly Cancelation in Field Theory and F-theory on a Circle

Abstract

We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.

48 pages, 2 figures; v2: typos corrected, comments on circle fluxes added

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• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• G4-Flux and Standard Model Vacua in F-theory
• Cardy Formula for 4d SUSY Theories and Localization
• Bootstrapping BPS spectra of 5d/6d field theories
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
• Algebraic Cycles and Local Anomalies in F-Theory
• Discrete Gauge Groups in F-theory Models on Genus-One Fibered Calabi-Yau 4-folds without Section
• Flopping and Slicing: SO(4) and Spin(4)-models
• Large U(1) charges in F-theory
• M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies
• 5d/6d Wilson loops from blowups
• The Toric SO(10) F-Theory Landscape
• Chiral anomalies on a circle and their cancellation in F-theory
• Mordell-Weil Torsion, Anomalies, and Phase Transitions
• The Geometry of SO(3), SO(5), and SO(6) models
• The Geometry of G${}_2$, Spin(7), and Spin(8)-models
• Gauge groups and matter spectra in F-theory compactifications on genus-one fibered Calabi-Yau 4-folds without section - hypersurface and double cover constructions
• Charge completeness and the massless charge lattice in F-theory models of supergravity
• One-modulus Calabi-Yau fourfold reductions with higher-derivative terms
• The Geometry of F${}_4$-Models
• Shift-symmetries and gauge coupling functions in orientifolds and F-theory
• Blowup Equations for Little Strings
• Generating functions for intersection products of divisors in resolved F-theory models
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• 6d $\mathcal{N}=(1,0)$ anomalies on $S^1$ and F-theory implications
• Chern-Simons couplings, modular duality, and anomaly cancellation in abelian F-theory