Towards Integrability of Topological Strings I: Three-forms on Calabi–Yau manifolds

Gerasimov, A.; Shatashvili, Samson L.

doi:10.1088/1126-6708/2004/11/074

Cited by 58 publications

(161 citation statements)

References 21 publications

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“…That is, if we have any PDE for our potential F , which is proved in its simplest case by the same argument as we have used for the simplest cases of Theorem 1 and Theorem 2 (to get out step by step of thick white points increasing the indices of vertices), then the argument described here immediately gives the full proof of this PDE. This corresponds in the theory of Gromov-Witten invariants to the lift of relations among strata in the moduli spaces of curves (for example, Getzler relation in M 1,4 gives us relations in M 1,5 , M 1,6 , and so on).…”

Section: Lemmamentioning

confidence: 99%

“…In fact, in order to obtain naturally the genus 0 part of our construction (i.e., Barannikov-Kontsevich solution in terms of trivalent trees) it is enough to study the BCOV-action written down in [3], [1,Appendix], [4], and [6]. But then we have to introduce 1/12-axiom just for computational reasons, and Getzler's relation in genus 1 comes over as a miracle.…”

Section: Pre-introductionmentioning

confidence: 99%

“…This is an immediate generalization of the Kodaira-Spenser theory of Bershadsky, Cecotti, Ooguri, and Vafa. However, the 1/12-axiom is missing in [3] and in all subsequent papers [4,6,5]. Barannikov and Kontsevich formulate and prove both propositions without using the representations of γ and F 0 in terms of graphs.…”

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confidence: 99%

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From Zwiebach Invariants to Getzler Relation

Losev

Shadrin

2007

Commun. Math. Phys.

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Abstract. We introduce the notion of Zwiebach invariants that generalize Gromov-Witten invariants and homotopical algebra structures. We outline the induction procedure that induces the structure of Zwiebach invariants on the subbicomplex, that gives the structure of Gromov-Witten invariants on subbicomplex with zero diffferentials. We propose to treat Hodge dGBV with 1/12 axiom as the simplest set of Zwiebach invariants, and explicitely prove that it induces WDVV and Getzler equations in genera 0 and 1 respectively.

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Section: Lemmamentioning

confidence: 99%

Section: Pre-introductionmentioning

confidence: 99%

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From Zwiebach Invariants to Getzler Relation

Losev

Shadrin

2007

Commun. Math. Phys.

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“…[41]) and by the path integral measure of the non-critical string (see e.g. [42] for a discussion). The topological string can be used to derive the physical couplings of N = 2 compactifications [24,25].…”

Section: Further Reading and Referencesmentioning

confidence: 99%

From Special Geometry to Black Hole Partition Functions

Mohaupt

2010

Springer Proceedings in Physics

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These notes are based on lectures given at the Erwin-Schrödinger Institut in Vienna in 2006/2007 and at the 2007 School on Attractor Mechanism in Frascati. Lecture I reviews special geometry from the superconformal point of view. Lecture II discusses the black hole attractor mechanism, the underlying variational principle and black hole partition functions. Lecture III applies the formalism introduced in the previous lectures to large and small BPS black holes in N = 4 supergravity. Lecture IV is devoted to the microscopic desription of these black holes in N = 4 string compactifications. The lecture notes include problems which allow the readers to develop some of the key ideas by themselves. Appendix A reviews special geometry from the mathematical point of view. Appendix B provides the necessary background in modular forms needed for understanding S-duality and string state counting.

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“…The B-model couples to a complex structure J on X. Its observables φ [8][9][10][11]. In genus zero, the extended moduli space of the B-model was studied in [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Topological strings in generalized complex space

Pestun¹

2007

Advances in Theoretical and Mathematical Physics

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A two-dimensional topological sigma-model on a generalized CalabiYau target space X is defined. The model is constructed in a BatalinVilkovisky formalism using only a generalized complex structure J and a pure spinor ρ on X. In the present construction, the algebra of Q-transformations automatically closes off-shell, the model transparently depends only on J , the algebra of observables and correlation functions for topologically trivial maps in genus zero are easily defined. The extended moduli space appears naturally. The familiar action of the twisted N = 2 conformal field theory (CFT) can be recovered after a gauge fixing. In the open case, we consider an example of generalized deformation of complex structure by a holomorphic Poisson bivector β and recover holomorphic noncommutative Kontsevich * -product.e-print archive: http://lanl.arXiv.org/abs/hep-th/0603145 1 On leave from ITEP, Moscow, 117259, Russia. VASILY PESTUN

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Towards Integrability of Topological Strings I: Three-forms on Calabi–Yau manifolds

Cited by 58 publications

References 21 publications

From Zwiebach Invariants to Getzler Relation

From Zwiebach Invariants to Getzler Relation

From Special Geometry to Black Hole Partition Functions

Topological strings in generalized complex space

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