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Global Anomalies and Geometric Engineering of Critical Theories in Six Dimensions

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arxiv hep-th/9703167 v2 pith:A472CRJX submitted 1997-03-24 hep-th

Michael Bershadsky , Cumrun Vafa This is my paper · ORCID
classification hep-th
keywords anomaliescouplingdimensionsf-theorygaugeglobalinfinitemodels
verification ladder T0 review T1 audit T2 compute T3 formal
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We show the existence of global gauge anomalies in six dimensions for gauge groups SU(2),SU(3) and G_2 coupled to matter, characterized by an element of Z_{12},Z_6 and Z_3 respectively. Consideration of this anomaly rules out some of the recently proposed 6 dimensional N=1 QFT's which were conjectured to possess IR fixed point at infinite coupling. We geometrically engineer essentially all the other models with one tensor multiplet using F-theory. In addition we construct 3 infinite series using F-theory geometry which do not have field theory analogs. All these models in the maximally Higgsed phase correspond to the strong coupling behaviour of E_8 x E_8 heterotic string compactification on K3 with instanton numbers (12+n,12-n).

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Global anomalies in $6D$ gauged supergravities

    hep-th 2025-07 conditional novelty 7.0 of 10

    New anomaly-free six-dimensional R-symmetry gauged supergravities are presented, and global anomaly freedom is shown to impose the constraints n_V ≡ 8 mod 12 (U(1)_R) and n_V = 60 (Sp(1)_R).

  2. Non-supersymmetric branes and discrete topological terms

    hep-th 2025-07 conditional novelty 6.0 of 10

    A direct computation from the tentative NS5-brane spectrum gives the opposite Z3 topological term (1/3 vs 2/3) from Tachikawa-Zhang, so the spectrum or the inflow interpretation must change.

  3. Machine Learning the 6d Supergravity Landscape

    hep-th 2025-05 conditional novelty 6.0 of 10

    An autoencoder and two neural classifiers, trained only on anomaly Gram matrices, provide automated clustering, outlier detection, and consistency predictions for millions of 6d supergravity building blocks.

  4. Rational points in the 6d supergravity landscape and simple current extensions

    hep-th 2026-03 unverdicted novelty 5.0 of 10

    Rationality of the 2d SCFT on BPS strings provides a consistency criterion that uniquely determines the elliptic genus and global gauge group in a class of 6d supergravity models without tensor multiplets.

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