Calabi–Yau quotients with terminal singularities

Favale, Filippo F.

doi:10.1007/s40574-017-0128-y

Cited by 4 publications

(3 citation statements)

References 9 publications

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“…This non-trivial prediction in fact agrees with Theorem 1.5 of [94], which implies that n O3 = 16 for all (strict) Calabi-Yau covering spaces. This mathematical result can also be explicitly checked in all the models of the database of [95].…”

Section: Jhep03(2023)197supporting

confidence: 82%

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Quantum gravity bounds on $$ \mathcal{N} $$ = 1 effective theories in four dimensions

Martucci

Risso

Weigand

2023

J. High Energ. Phys.

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We propose quantum gravitational constraints on effective four-dimensional theories with $$ \mathcal{N} $$ N = 1 supersymmetry. These Swampland constraints arise by demanding consistency of the worldsheet theory of a class of axionic, or EFT, strings whose existence follows from the Completeness Conjecture of quantum gravity. Modulo certain assumptions, we derive positivity bounds and quantization conditions for the axionic couplings to the gauge and gravitational sector at the two- and four-derivative level, respectively. We furthermore obtain general bounds on the rank of the gauge sector in terms of the gravitational couplings to the axions. We exemplify how these bounds rule out otherwise consistent effective supergravity theories as theories of quantum gravity. Our derivations of the quantum gravity bounds are tested and further motivated in concrete string theoretic settings. In particular, this leads to a sharper version of the bound on the gauge group rank in F-theory on elliptic four-folds with a smooth base, which improves the known geometrical Kodaira bounds. We furthermore provide a detailed derivation of the EFT string constraints in heterotic string compactifications including higher derivative corrections to the effective action and apply the bounds to M-theory compactifications on G2 manifolds.

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Section: Jhep03(2023)197supporting

confidence: 82%

“…We thank X. Gao and in particular F. Carta and R. Valandro for discussions on the available examples of Calabi-Yau orientifolds with just O3 planes. We also thank F. Carta for helping us in checking (6.54) by scanning the database[95], and for pointing out to us reference[94].…”

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confidence: 99%

Quantum gravity bounds on $$ \mathcal{N} $$ = 1 effective theories in four dimensions

Martucci

Risso

Weigand

2023

J. High Energ. Phys.

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“…As a consequence of a result 3 in [14], we deduce that L 1 is a symplectic subgroup of Aut(Ỹ ). In fact g acts freely onỸ (by direct check inside the torus and using the Lemma for the outside) and h is an involution that fixes curves.…”

Section: Corollary 42 For Every Maximal Projective Subdivisionx Of mentioning

confidence: 63%

A closer look at mirrors and quotients of Calabi-Yau threefolds

Bini¹,

Favale²

2016

Annali Scuola Normale Superiore - Classe Di Scienze

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Let X be the toric variety (P 1 ) 4 associated with its four-dimensional polytope 1. Denote byX the resolution of the singular Fano variety X o associated with the dual polytope 1 o . Generically, anticanonical sections Y of X and anticanonical sectionsỸ ofX are mirror partners in the sense of Batyrev. Our main result is the following: the Hodge-theoretic mirror of the quotient Z associated to a maximal admissible pair (Y, G) in X is not a quotientZ associated to an admissible pair inX. Nevertheless, it is possible to construct a mirror orbifold for Z by means of a quotient of a suitableỸ . Its crepant resolution is a Calabi-Yau threefold with Hodge numbers (8, 4). Instead, if we start from a non-maximal admissible pair, in the same case, its mirror is the quotient associated to an admissible pair.

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