# Topological Open Strings on Orbifolds

@article{Bouchard2010TopologicalOS, title={Topological Open Strings on Orbifolds}, author={Vincent Bouchard and Albrecht Klemm and Marcos Mari{\~n}o and Sara Pasquetti}, journal={Communications in Mathematical Physics}, year={2010}, volume={296}, pages={589-623} }

We use the remodeling approach to the B-model topological string in terms of recursion relations to study open string amplitudes at orbifold points. To this end, we clarify modular properties of the open amplitudes and rewrite them in a form that makes their transformation properties under the modular group manifest. We exemplify this procedure for the $${{\mathbb C}^3/{\mathbb Z}_3}$$ orbifold point of local $${{\mathbb P}^2}$$, where we present results for topological string amplitudes for…

## 55 Citations

Open orbifold Gromov-Witten invariants of $${[\mathbb{C}^3/\mathbb{Z}_n]}$$: localization and mirror symmetry

- Mathematics
- 2010

We develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of $${[\mathbb{C}^3/\mathbb{Z}_n]}$$ and provide extensive checks with predictions from open string…

Open Topological Strings and Integrable Hierarchies: Remodeling the A-Model

- Mathematics
- 2011

We set up, purely in A-model terms, a novel formalism for the global solution of the open and closed topological A-model on toric Calabi-Yau threefolds. The starting point is to build on recent…

Topological string amplitudes for the local $\frac{1}{2}$K3 surface

- Mathematics
- 2017

We study topological string amplitudes for the local half K3 surface. We develop a method of computing higher-genus amplitudes along the lines of the direct integration formalism, making full use of…

Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model

- Mathematics
- 2009

Equivariant Gromov-Witten Theory of GKM Orbifolds

- Mathematics
- 2015

In this paper, we study the all genus Gromov-Witten theory for any GKM orbifold $X$. We generalize the Givental formula which is studied in the smooth case in \cite{Giv2} \cite{Giv3} \cite{Giv4} to…

Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String

- Mathematics, Physics
- 2010

Following a recent paper by Alday and Tachikawa, we compute the instanton partition function in the presence of the surface operator by the localization formula on the moduli space. For SU(2)…

A& B model approaches to surface operators and Toda thoeries

- Mathematics
- 2010

It has recently been argued [1] that the inclusion of surface operators in 4d$ \mathcal{N} = 2 $ SU(2) quiver gauge theories should correspond to insertions of certain degenerate operators in the…

Deformed planar topological open string amplitudes on Seiberg-Witten curve

- Geology
- 2012

A bstractWe study refined B-model via the beta ensemble of matrix models. Especially, for four dimensional $ \mathcal{N} = 2 $ SU(2) supersymmetric gauge theories with Nf = 0,1 and 2 fundamental…

Crepant resolutions and open strings

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2019

Abstract In the present paper, we formulate a Crepant Resolution Correspondence for open Gromov–Witten invariants (OCRC) of toric Lagrangian branes inside Calabi–Yau 3-orbifolds by encoding the open…

On the remodeling conjecture for toric Calabi-Yau 3-orbifolds

- MathematicsJournal of the American Mathematical Society
- 2019

The Remodeling Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti (BKMP) relates the A-model open and closed topological string amplitudes (the all genus open and closed Gromov-Witten invariants)…

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