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Topological string theory

About: Topological string theory is a research topic. Over the lifetime, 1206 publications have been published within this topic receiving 54758 citations.


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TL;DR: In this article, it was shown that the quantum eigenvalue problem for a particular Calabi-Yau manifold is closely related to the Hofstadter problem for electrons on a two-dimensional square lattice.
Abstract: The B-model approach of topological string theory leads to difference equations by quantizing algebraic mirror curves. It is known that these quantum mechanical systems are solved by the refined topological strings. Recently, it was pointed out that the quantum eigenvalue problem for a particular Calabi--Yau manifold, known as local $\mathbb{F}_0$, is closely related to the Hofstadter problem for electrons on a two-dimensional square lattice. In this paper, we generalize this idea to a more complicated Calabi--Yau manifold. We find that the local $\mathcal{B}_3$ geometry, which is a three-point blow-up of local $\mathbb{P}^2$, is associated with electrons on a triangular lattice. This correspondence allows us to use known results in condensed matter physics to investigate the quantum geometry of the toric Calabi--Yau manifold.

4 citations

Journal ArticleDOI
TL;DR: In this article, the SO(2,2) Lorentz invariance of the classical N = 2 string was restored in the N = 4 topological formalism by Berkovits and Vafa.

4 citations

Book ChapterDOI
TL;DR: The instanton partition function of supersymmetric gauge theory in the general ε-background is, in a suitable analytic continuation, a solution of the holomorphic anomaly equation known from B-model topological strings as mentioned in this paper.
Abstract: The instanton partition function of \(\mathcal{N}=2\) gauge theory in the general \(\Omega \)-background is, in a suitable analytic continuation, a solution of the holomorphic anomaly equation known from B-model topological strings. The present review of this connection is a contribution to a special volume on recent developments in \(\mathcal{N}=2\) supersymmetric gauge theory and the 2d-4d relation, edited by J. Teschner.

4 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated 2D quantum gravity in the conventional formalism of conformal field theory (CFT) and showed that the value c=−2 seems distinguished in such a continual theory, just as it does in the lattice and topological approaches to 2D gravity.

4 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the BRS operator of the topological string B model is not holomorphic in the complex structure of the target space, which implies that the so-called holomorphic anomaly of topological strings should not be interpreted as a BRS anomaly.
Abstract: We show that the BRS operator of the topological string B model is not holomorphic in the complex structure of the target space. This implies that the so-called holomorphic anomaly of topological strings should not be interpreted as a BRS anomaly.

4 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20235
20228
202115
202012
201915
201817