Related papers: Open strings on knot complements
We study resurgence for some 3-manifold invariants when $G_{\mathbb{C}}=SL(2, \mathbb{C})$. We discuss the case of an infinite family of Seifert manifolds for general roots of unity and the case of the torus knot complement in $S^3$. Via…
Progress in identifying the bulk microstate interpretation of the Ryu-Takayanagi formula requires understanding how to define entanglement entropy in the bulk closed string theory. Unfortunately, entanglement and Hilbert space factorization…
We propose a mirror derivation of the quiver description of open topological strings known as the knots-quivers correspondence, based on enumerative invariants of augmentation curves encoded by exponential networks. Quivers are obtained by…
In this manuscript we introduce a method to measure entanglement of curves in 3-space that extends the notion of knot and link polynomials to open curves. We define the bracket polynomial of curves in 3-space and show that it has real…
We propose a geometric characterisation of the topological string partition functions associated to the local Calabi-Yau (CY) manifolds used in the geometric engineering of $d=4$, $\mathcal{N}=2$ supersymmetric field theories of class…
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…
It has been recently conjectured that the exact eigenfunctions of quantum mirror curves can be obtained by combining their WKB expansion with the open topological string wavefunction. In this paper we give further evidence for this…
The open topological string partition function in the background of a D-brane on a Calabi-Yau threefold specifies a state in the Hilbert space associated with the quantization of the underlying special geometry. This statement is a…
We compute the dimensions of $\text{GL}_N$-skein modules of genus-one mapping tori $T^2\times_\gamma S^1$, for an arbitrary diffeomorphism of $T^2$, and for generic quantum parameter. These are most cleanly expressed via a generating…
Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371…
We discuss a matrix of periodic holomorphic functions in the upper and lower half-plane which can be obtained from a factorization of an Andersen-Kashaev state integral of a knot complement with remarkable analytic and asymptotic properties…
We study factorizations of topological string amplitudes on higher genus Riemann surfaces with multiple boundary components and find quantum A-infinity relations, which are the higher genus analog of the (classical) A-infinity relations on…
Given a 3-manifold $M$, and a branched cover arising from the projection of a Lagrangian 3-manifold $L$ in the cotangent bundle of $M$ to the zero-section, we define a map from the skein of $M$ to the skein of $L$, via the skein-valued…
This paper gives the first explicit, two-sided estimates on the cusp area of once-punctured torus bundles, 4-punctured sphere bundles, and 2-bridge link complements. The input for these estimates is purely combinatorial data coming from the…
This article consists of two parts. In Part 1, we present a formulation of two-dimensional topological quantum field theories in terms of a functor from a category of Ribbon graphs to the endofuntor category of a monoidal category. The key…
We study the stringy genus one partition function of $N=2$ SCFT's. It is shown how to compute this using an anomaly in decoupling of BRST trivial states from the partition function. A particular limit of this partition function yields the…
It has recently been conjectured that the closed topological string wave function computes a grand canonical partition function of BPS black hole states in 4 dimensions: Z_BH=|psi_top|^2. We conjecture that the open topological string wave…
We consider branes in refined topological strings. We argue that their wave-functions satisfy a Schr\"odinger equation depending on multiple times and prove this in the case where the topological string has a dual matrix model description.…
This paper proves quantum modularity of both functions from $\mathbb{Q}$ and $q$-series associated to the closed manifold obtained by $-\frac{1}{2}$ surgery on the figure-eight knot, $4_1(-1,2)$. In a sense, this is a companion to work of…
We continue the study of positive geometries underlying the {\it Grassmannian string integrals}, which are a class of "stringy canonical forms", or stringy integrals, over the positive Grassmannian mod torus action, $G_+(k,n)/T$. The…