On solutions to Walcher’s extended holomorphic anomaly equation

This work is concerned with branes and differential equations for oneparameter Calabi-Yau hypersurfaces in weighted projective spaces. For a certain class of B-branes, we derive the inhomogeneous Picard-Fuchs equations satisfied by the brane superpotential. In this way, we arrive at a prediction for the real BPS invariants for holomorphic maps of worldsheets with low Euler characteristics, ending on the mirror A-branes.

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“…Indeed, we find 19) which is consistent with W eff = 0. Therefore, we conclude that this brane has one unobstructed boundary modulus.…”

Section: The D = 8 Brane L = (3 3 2 1 0)supporting

confidence: 77%

“…Further work includes [16][17][18][19][20] In the first paper, [10], disk instantons have been computed for the quintic using mostly A-model techniques. A particular Lagrangian A-brane, defined by the real quintic, was identified.…”

Section: Introductionmentioning

confidence: 99%

Towards open string mirror symmetry for one-parameter Calabi-Yau hypersurfaces

Knapp

Scheidegger

2009

Advances in Theoretical and Mathematical Physics

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“…Having a powerful alternative computation method could help pushing forward the understanding in some directions which have been explored recently. The polynomial construction of topological string amplitudes applies also to compactifications with background D-branes [35,2,36]. It should be straightfoward to work out the corresponding boundary conditions also for this case and fix the holomorphic ambiguity along the lines of the above arguments.…”

Section: Resultsmentioning

confidence: 99%

Global properties of topological string amplitudes and orbifold invariants

Alim¹,

Länge²,

Mayr³

2010

J. High Energ. Phys.

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We derive topological string amplitudes on local Calabi-Yau manifolds in terms of polynomials in finitely many generators of special functions. These objects are defined globally in the moduli space and lead to a description of mirror symmetry at any point in the moduli space. Holomorphic ambiguities of the anomaly equations are fixed by global information obtained from boundary conditions at few special divisors in the moduli space. As an illustration we compute higher genus orbifold Gromov-Witten invariants for

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“…Similar equations, which can in fact be understood as a special case of the equations of [8], were obtained in [9,10] from the study of matrix models. Earlier work on the holomorphic anomaly in the open string appears in [2,11]; more recent work includes [12][13][14][15]. For the wavefunction interpretation of the open topological string along the lines of [16], see [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Evidence for tadpole cancelation in the topological string

Walcher

2009

Communications in Number Theory and Physics

120

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We study the topological string on compact Calabi-Yau threefolds in the presence of orientifolds and D-branes. In examples, we find that the total topological string amplitude admits a Bogomol'nyiPrasad-Sommerfield (BPS) expansion only if the topological charge of the D-brane configuration is equal to that of the orientifold plane. We interpret this as a manifestation of a general tadpole cancellation condition in the topological string that is necessary for decoupling A-and B-model in loop amplitudes. Our calculations in the A-model involve an adapted version of existing localization techniques, and give predictions for the real enumerative geometry of higher genus curves in Calabi-Yau manifolds. In the B-model, we introduce an extension of the holomorphic anomaly equation to unoriented strings.

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On solutions to Walcher’s extended holomorphic anomaly equation

Abstract: We give a generalization of Yamaguchi-Yau's result to Walcher's extended holomorphic anomaly equation.

Cited by 7 publications

References 21 publications

Towards open string mirror symmetry for one-parameter Calabi-Yau hypersurfaces

Towards open string mirror symmetry for one-parameter Calabi-Yau hypersurfaces

Global properties of topological string amplitudes and orbifold invariants

Evidence for tadpole cancelation in the topological string

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