8d gauge anomalies and the topological Green-Schwarz mechanism

García-Etxebarria, Iñaki; Hayashi, Hirotaka; Ohmori, Kantaro; Tachikawa, Yuji; Yonekura, Kazuya

doi:10.1007/jhep11(2017)177

Cited by 65 publications

(124 citation statements)

References 43 publications

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“…They also do not admit a (geometric) heterotic dual due to their rigidity and the fact that their minimal gauge group does not fit into E 8 × E 8 (or SO (32)) . It would be interesting, to investigate those eight dimensional exceptions from a field theoretical perspective, maybe in the spirit of [75]. Finally, since all admissible torsion groups must be embeddable into a rational elliptic surface (and into its E 8 lattice) it seems plausible, that the heterotic string plays a similar prominent role as in [68] to explain the constraints we find from the F-theory perspective.…”

Section: Discussionmentioning

confidence: 90%

Modular curves and Mordell-Weil torsion in F-theory

Hajouji

Oehlmann

2020

J. High Energ. Phys.

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In this work we prove a bound for the torsion in Mordell-Weil groups of smooth elliptically fibered Calabi-Yau 3-and 4-folds. In particular, we show that the set which can occur on a smooth elliptic Calabi-Yau n-fold for (n ≥ 3) is contained in the set of subgroups which appear on a rational elliptic surface, and is slightly larger for n = 2. The key idea in our proof is showing that any elliptic fibration with sufficiently large torsion has singularities in codimension 2 which do not admit a crepant resolution. We prove this by explicitly constructing and studying maps to a modular curve whose existence is predicted by a universal property. We use the geometry of modular curves to explain the minimal singularities that appear on an elliptic fibration with prescribed torsion, and to determine the degree of the fundamental line bundle (hence the Kodaira dimension) of the universal elliptic surface which we show to be consistent with explicit Weierstrass models. The constraints from the modular curves are used to bound the fundamental group of any gauge group G in a supergravity theory obtained from F-theory. We comment on the isolated 8-dimensional theories, obtained from extremal K3's, that are able to circumvent lower dimensional bounds. These theories neither have a heterotic dual, nor can they be compactified to lower dimensional minimal SUGRA theories. We also comment on the maximal, discrete gauged symmetries obtained from certain Calabi-Yau threefold quotients.

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Section: Discussionmentioning

confidence: 90%

Modular curves and Mordell-Weil torsion in F-theory

Hajouji

Oehlmann

2020

J. High Energ. Phys.

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“…In this paper we have only considered fSPTs with finite group G. On the other hand, in [39] it is proposed that a particular 9d Sp(N ) fSPT should have boundary TQFT. It would be intriguing if the method in this section can be generalized into the continuous group case.…”

Section: General Structure and Commentsmentioning

confidence: 99%

Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms

Guo

Ohmori

Putrov

et al. 2020

Commun. Math. Phys.

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We formulate a family of spin Topological Quantum Filed Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf-Witten TQFTs. They are obtained by gauging G-equivariant invertible spin-TQFTs, or, in physics language, gauging the interacting fermionic Symmetry Protected Topological states (SPTs) with a finite group G symmetry. We use the fact that the latter are classified by Pontryagin duals to spin-bordism groups of the classifying space BG. We also consider unoriented analogues, that is G-equivariant invertible pin ± -TQFTs (fermionic time-reversal-SPTs) and their gauging. We compute these groups for various examples of abelian G using Adams spectral sequence and describe all corresponding TQFTs via certain bordism invariants in dimensions 3, 4, and other. This gives explicit formulas for the partition functions of spin-TQFTs on closed manifolds with possible extended operators inserted. The results also provide explicit classification of 't Hooft anomalies of fermionic QFTs with finite abelian group symmetries in one dimension lower. We construct new anomalous boundary deconfined spin-TQFTs (surface fermionic topological orders). We explore SPT and SET (symmetry enriched topologically ordered) states, and crystalline SPTs protected by space-group (e.g. translation Z) or point-group (e.g. reflection, inversion or rotation C m ) symmetries, via the layer-stacking construction. *

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“…This is a (p−1)-form K-gauge theory 3 , and couples to a (q+1)-form K-symmetry background A and a (p+1)-form K-symmetry background B. 4 This theory has an anomaly N B ∪ A. Our case (2.4) is when p = 1, A = g * z and B = g * e. This means that the symmetry extension method can be generalized so that the symmetry is extended by a higher-form symmetry.…”

Section: Extension By Higher-form Symmetriesmentioning

confidence: 99%

On gapped boundaries for SPT phases beyond group cohomology

Kobayashi

Ohmori

Tachikawa

2019

J. High Energ. Phys.

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We discuss a strategy to construct gapped boundaries for a large class of symmetry-protected topological phases (SPT phases) beyond group cohomology. This is done by a generalization of the symmetry extension method previously used for cohomological SPT phases. We find that this method allows us to construct gapped boundaries for time-reversal-invariant bosonic SPT phases and for fermionic Gu-Wen SPT phases for arbitrary finite internal symmetry groups.

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8d gauge anomalies and the topological Green-Schwarz mechanism

Cited by 65 publications

References 43 publications

Modular curves and Mordell-Weil torsion in F-theory

Modular curves and Mordell-Weil torsion in F-theory

Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms

On gapped boundaries for SPT phases beyond group cohomology

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