Topological strings on elliptic fibrations

Alim, Murad; Scheidegger, Emanuel

doi:10.4310/cntp.2014.v8.n4.a4

Cited by 50 publications

(141 citation statements)

References 66 publications

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“…This by itself is analogous to what has been done in six dimensions [65][66][67], where the modular geometry of elliptic three-folds [103][104][105] becomes important. However, we will see that the situation is much more complicated than in six dimensions.…”

Section: General Properties Of the 4d Elliptic Genussupporting

confidence: 52%

Modular fluxes, elliptic genera, and weak gravity conjectures in four dimensions

Lee

Lerche

Weigand

2019

J. High Energ. Phys.

203

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We analyse the Weak Gravity Conjecture for chiral four-dimensional F-theory compactifications with N = 1 supersymmetry. Extending our previous work on nearly tensionless heterotic strings in six dimensions, we show that under certain assumptions a tower of asymptotically massless states arises in the limit of vanishing coupling of a U (1) gauge symmetry coupled to gravity. This tower contains super-extremal states whose charge-tomass ratios are larger than those of certain extremal dilatonic Reissner-Nordström black holes, precisely as required by the Weak Gravity Conjecture. Unlike in six dimensions, the tower of super-extremal states does not always populate a charge sub-lattice.The main tool for our analysis is the elliptic genus of the emergent heterotic string in the chiral N = 1 supersymmetric effective theories. This also governs situations where the heterotic string is non-perturbative. We show how it can be computed in terms of BPS invariants on elliptic four-folds, by making use of various dualities and mirror symmetry. Compared to six dimensions, the geometry of the relevant elliptically fibered four-folds is substantially richer than that of the three-folds, and we classify the possibilities for obtaining critical, nearly tensionless heterotic strings. We find that the (quasi-)modular properties of the elliptic genus crucially depend on the choice of flux background. Our general results are illustrated in a detailed example. seung.joo.lee, wolfgang.lerche, timo.weigand @cern.ch arXiv:1901.08065v1 [hep-th] 23 Jan 2019 F Example of an emergent critical string in a Type B weak coupling limit 62 Table B.2: GLSM charges of the toric coordinates of the four-fold Y 4 that is an elliptic fibration over the base three-fold B 3 , which by itself is described in Table B.1.Here, each of the generators is described in terms of its intersection numbers with the 10 toric divisors d ρ := {ν ρ = 0}, for ρ = x 0 , · · · , s, where we keep the same ordering as in Table B.2. The (closure of the) Kähler cone K(Y 4 ) is then spanned by the divisor classes, where l (a) J b = δ a b for a, b = 1, . . . , 5. Note that three of the generators J 1 , J 2 , and J 4 of K(Y 4 ) are respectively pull-backs of the generators j 1 , j 2 , and j 3 in (B.6) of K(B 3 ), where, by slight abuse of notation, the base toric divisors and their pull-backs are denoted by the same symbols. Finally, the intersection polynomial is given as I(Y 4 ) = 10J 1 2 J 3 2 + 46J 2 2 J 3 2 + 262J 3 4 + 16J 3 2 J 4 2 + 4J 1 2 J 5 2 + 20J 2 2 J 5 2 + 134J 3 2 J 5 2 + 8J 4 2 J 5 2 + 52J 5 4 + 57J 3 3

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Section: General Properties Of the 4d Elliptic Genussupporting

confidence: 52%

Modular fluxes, elliptic genera, and weak gravity conjectures in four dimensions

Lee

Lerche

Weigand

2019

J. High Energ. Phys.

203

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“…(1.2) From this action they were able to deduce that the Yukawa-coupling C τ τ τ is in the limit Imt → ∞ proportional to the Eisenstein series E 4 (τ ). In subsequent works the understanding of the modular properties of the topological string partition function on non-compact [16,17] and compact elliptic fibrations has been significantly improved upon [18,19]. Most importantly it was found that the modular structure extends to arbitary base degree and that the holomorphic anomaly equations found by [20] imply a "modular recursion" in terms of the base degree and the worldsheet genus.…”

Section: Introductionmentioning

confidence: 99%

Modularity from monodromy

Schimannek

2019

J. High Energ. Phys.

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In this note we describe a method to calculate the action of a particular Fourier-Mukai transformation on a basis of brane charges on elliptically fibered Calabi-Yau threefolds with and without a section. The Fourier-Mukai kernel is the ideal sheaf of the relative diagonal and for fibrations that admit a section this is essentially the Poincar sheaf. We find that in this case it induces an action of the modular group on the charges of 2-branes.

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“…A general classification of toric and nontoric base manifolds in Ftheory models was discussed in [24,25] and, more recently, in [26]. For general properties of topological strings on elliptic Calabi-Yau threefolds, see [27][28][29].…”

Section: Little Strings and Dual Brane Websmentioning

confidence: 99%

Dual little strings and their partition functions

et al. 2018

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We study the topological string partition function of a class of toric, double elliptically fibered Calabi-Yau threefolds X N;M at a generic point in the Kähler moduli space. These manifolds engineer little string theories in five dimensions or lower and are dual to stacks of M5-branes probing a transverse orbifold singularity. Using the refined topological vertex formalism, we explicitly calculate a generic building block which allows us to compute the topological string partition function of X N;M as a series expansion in different Kähler parameters. Using this result, we give further explicit proof for a duality found previously in the literature, which relates X N;M ∼ X N 0 ;M 0 for NM ¼ N 0 M 0 and gcdðN; MÞ ¼ gcdðN 0 ; M 0 Þ.

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Topological strings on elliptic fibrations

Cited by 50 publications

References 66 publications

Modular fluxes, elliptic genera, and weak gravity conjectures in four dimensions

Modular fluxes, elliptic genera, and weak gravity conjectures in four dimensions

Modularity from monodromy

Dual little strings and their partition functions

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