Related papers: Refining the Shifted Topological Vertex
We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5-branes, using the refined topological vertex on the dual Calabi-Yau threefolds. The theories include certain non-Lagrangian theories such as the T_N…
We introduce a refined version of the 3D index for 3-manifolds, building on the construction of the 3D $\mathcal{N}=2$ gauge theory $T[M]$ by Dimofte-Gaiotto-Gukov and Gang-Yonekura. The refined index is a superconformal index of $T[M]$…
It has been argued that the Nekrasov's partition function gives the generating function of refined BPS state counting in the compactification of M theory on local Calabi-Yau spaces. We show that a refined version of the topological vertex…
We consider the issue of the slice invariance of refined topological string amplitudes, which means that they are independent of the choice of the preferred direction of the refined topological vertex. We work out two examples. The first…
We use mirror symmetry, the refined holomorphic anomaly equation and modularity properties of elliptic singularities to calculate the refined BPS invariants of stable pairs on non-compact Calabi-Yau manifolds, based on del Pezzo surfaces…
In this paper we propose a definition of torsion refined Gopakumar-Vafa (GV) invariants for Calabi-Yau threefolds with terminal nodal singularities that do not admit K\"ahler crepant resolutions. Physically, the refinement takes into…
We study properties of the recently established refined topological recursion for some simple spectral curves associated to quadratic differentials. We prove explicit formulas for the free energy and Voros coefficients of the corresponding…
We present the partition function of the refined Chern-Simons theory on $S^3$ with arbitrary A,B,C,D gauge algebra in terms of multiple sine functions. For B and C cases this representation is novel. It allows us to conjecture duality to…
In this work we verify consistency of refined topological string theory from several perspectives. First, we advance the method of computing refined open amplitudes by means of geometric transitions. Based on such computations we show that…
In this article, we calculated the refined topological vertex for the one parameter case using the Jack symmetric functions. Also, we obtain the partition function for elliptic N=2 models, the results coincide with those of Nekrasov…
Open topological string partition function gives rise to open Gromov-Witten invariants, open Donaldson-Thomas invariants and 3D-5D BPS indices. Utilizing the remodelling conjecture which connects topological recursion and topological string…
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…
Reshetikhin-Turaev (a.k.a. Chern-Simons) TQFT is a functor that associates vector spaces to two-dimensional genus g surfaces and linear operators to automorphisms of surfaces. The purpose of this paper is to demonstrate that there exists a…
Antoniadis et al proposed a relation between the Omega-deformation and refined correlation functions of the topological string theory. We investigate the proposal for the deformed conifold geometry from a non-compact Gepner model approach.…
In this paper we develop the Hermitian refinement of symplectic Clifford analysis, by introducing a complex structure $\mathbb{J}$ on the canonical symplectic manifold $(\mathbb {R}^{2n},\omega_0)$. This gives rise to two symplectic Dirac…
We show here that the refined theorems for both lecture hall partitions and anti-lecture hall compositions can be obtained as straightforward consequences of two q-Chu Vandermonde identities, once an appropriate recurrence is derived. We…
We propose a new fermionic sum formula for the Macdonald index of a class of Argyres-Douglas theories. The formula arises naturally from a three-dimensional topological field theory obtained via a twisted dimensional reduction of the 4d…
We construct string topology operations in twisted K-theory. We study the examples given by symplectic Grassmannians, computing the twisted K-theory of the loop spaces of quaternionic projective spaces in detail. Via the work of…
The closed topological vertex is the simplest ``off-strip'' case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory…
The convolution quadrature theory is a systematic approach to analyse the approximation of the Riemann-Liouville fractional operator $I^{\alpha}$ at node $x_{n}$. In this paper, we develop the shifted convolution quadrature ($SCQ$) theory…