Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions

By Min-xin Huang, A. Klemm, Seth Quackenbush. 2006

220 citations recorded by the source corpus.

The topological string partition function Z(λ,t,t) =exp(λ2 g-2 Fg(t, t)) is calculated on a compact Calabi–Yau M. The Fg(t, t) fulfil the holomorphic anomaly equations, which imply that ψ=Z transforms as a wave function on the symplectic space H3(M, Z). This defines it everywhere in the moduli space M(M) along with preferred local coordinates. Modular properties of the sections Fg as well as local constraints from the 4d effective action allow us to fix Z to a large extent. Currently with a newly found gap condition at the conifold, regularity at the orbifold and the most naive bounds from Castelnuovo’s theory, we can provide the boundary data, which specify Z, e.g. up to genus 51 for the quintic.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7b30f39f006d7c6e7e97ef4221c722cb593694af

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In Geometry and Topology

1. Marcos Mariño
2. A. Klemm
3. V. Bouchard
4. Sara Pasquetti
5. Min-xin Huang
6. Y. Ruan
7. A. Chiodo
8. G. Moore

In Nuclear and High Energy Physics

1. Marcos Mariño
2. A. Klemm
3. Thomas W. Grimm
4. F. Quevedo
5. M. Cicoli
6. Eran Palti
7. Min-xin Huang
8. C. Vafa

Citations in the corpus

• Direct integration of the topological string (2007, background): “where tD is a suitable coordinate transverse to the conifold divisor [34].”
• Remodeling the B-Model (2007, background): “In the compact case they allow to calculate closed string amplitudes to high, but finite genus (for example, g = 51 for the quintic) [33].”
• Explicit de Sitter flux vacua for global string models with chiral matter (2013, background): “with c2(M3) denoting the second Chern class of M̃3 [107].”
• The Witten equation, mirror symmetry and quantum singularity theory (2007, unknown): “(For some recent advances, see [HKQ09].”
• Landau–Ginzburg/Calabi–Yau correspondence for quintic three-folds via symplectic transformations (2008, methodology): “and coincide with the period integrals at the Gepner point computed by Huang, Klemm, and Quackenbush [ 24 ].”
• The Ω Deformed B-model for Rigid N = 2 Theories (2011, methodology): “The relation between the holomorphic anomaly and target space modularity was developed in [10, 42] and led, upon imposing suitable boundary conditions, to the direct integration method [11, 12, 14, 9].”
• Split states, entropy enigmas, holes and halos (2007, background): “order Q, and despite tremendous recent progress [102], the available data so far are not yet sufficient to get even a numerical hint of what the correct answer could be.”
• Refined stable pair invariants for E-, M- and [p, q]-strings (2013, methodology): “One can fix the holomorphic ambiguity using the gap boundary conditions proposed in [76, 78].”