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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 paper, the β-deformed matrix models using the method of refined topological string theory were studied and exact test of the quantum integrality conjecture in the Nekrasov-Shatashvili limit was provided.
Abstract: We study the β-deformed matrix models using the method of refined topological string theory. The refined holomorphic anomaly equation and boundary conditions near the singular divisors of the underlying geometry fix the refined amplitudes recursively. We provide exact test of the quantum integrality conjecture in the Nekrasov-Shatashvili limit. We check the higher genus exact formulae with perturbative matrix model calculations.
5 citations
5 citations
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TL;DR: In this article, a summary of the applications of duality to Donaldson-Witten theory and its generalizations is presented, with a special emphasis on the computation of Donaldson invariants in terms of Seiberg-witten invariants using recent results in N=2 supersymmetric gauge theory.
Abstract: We present a summary of the applications of duality to Donaldson-Witten theory and its generalizations Special emphasis is made on the computation of Donaldson invariants in terms of Seiberg-Witten invariants using recent results in N=2 supersymmetric gauge theory A brief account on the invariants obtained in the theory of non-abelian monopoles is also presented
5 citations
TL;DR: In this article, the perspective of Kac-Schwarz operators is introduced to the authors' previous work on the quantum mirror curves of topological string theory in strip geometry and closed topological vertex.
Abstract: The perspective of Kac-Schwarz operators is introduced to the authors' previous work on the quantum mirror curves of topological string theory in strip geometry and closed topological vertex. Open string amplitudes on each leg of the web diagram of such geometry can be packed into a multi-variate generating function. This generating function turns out to be a tau function of the KP hierarchy. The tau function has a fermionic expression, from which one finds a vector $|W\rangle$ in the fermionic Fock space that represents a point $W$ of the Sato Grassmannian. $|W\rangle$ is generated from the vacuum vector $|0\rangle$ by an operator $g$ on the Fock space. $g$ determines an operator $G$ on the space $V = \mathbb{C}((x))$ of Laurent series in which $W$ is realized as a linear subspace. $G$ generates an admissible basis $\{\Phi_j(x)\}_{j=0}^\infty$ of $W$. $q$-difference analogues $A$, $B$ of Kac-Schwarz operators are defined with the aid of $G$. $\Phi_j(x)$'s satisfy the linear equations $A\Phi_j(x) = q^j\Phi_j(x)$, $B\Phi_j(x) = \Phi_{j+1}(x)$. The lowest equation $A\Phi_0(x) = \Phi_0(x)$ reproduces the quantum mirror curve in the authors' previous work.
5 citations
TL;DR: In this paper, a unified formulation of the quantization of string and the space-time symmetry is given. But this formulation is based on the Hopf algebra structure in string worldsheet theory.
Abstract: We investigate the Hopf algebra structure in string worldsheet theory and give a unified formulation of the quantization of string and the space-time symmetry. We reformulate the path integral quantization of string as a Drinfeld twist at the worldsheet level. The coboundary relation shows that the Drinfeld twist defines a module algebra which is equivalent to operators with normal ordering. Upon applying the twist, the space-time diffeomorphism
5 citations