Related papers: From quantum curves to topological string partitio…
We initiate the study of wall crossing phenomena in orientifolds of local toric Calabi-Yau 3-folds from a topological string perspective. For this purpose, we define a notion of real Donaldson-Thomas partition function at the large volume,…
These are lecture notes on non-K\"ahler complex threefolds presented at the MATRIX program ``The geometry of moduli spaces in string theory''. We review some basics of Calabi-Yau geometry in Section 1, describe topological features of the…
We study the quantum volume of D-branes wrapped around various cycles in Calabi-Yau manifolds, as the manifold's moduli are varied. In particular, we focus on the behaviour of these D-branes near phase transitions between distinct low…
We study topological string theory on elliptically fibered Calabi-Yau threefolds using mirror symmetry. We compute higher genus topological string amplitudes and express these in terms of polynomials of functions constructed from the…
Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmology. We present a straightforward approach to calculate the…
We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper-elliptic curve. We express this quantum curve in terms of…
The moduli space of multiply-connected Calabi-Yau threefolds is shown to contain codimension-one loci on which the corresponding variety develops a certain type of hyperquotient singularity. These have local descriptions as discrete…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
We describe a family of twisted partition functions for the relativistic spinning particle models. For suitable choices of fugacities this computes a refined Euler characteristics that counts the dimension of the physical states for…
We investigate quantum corrections to the classical four-dimensional low-energy effective action of type II string theory compactified on SU(3) structure geometries. Various methods previously developed for Calabi-Yau compactifications are…
We consider the real topological string on certain non-compact toric Calabi-Yau three-folds X, in its physical realization describing an orientifold of type IIA on X with an O4-plane and a single D4-brane stuck on top. The orientifold can…
We show that topological strings on a class of non-compact Calabi-Yau threefolds is equivalent to two dimensional bosonic U(N) Yang-Mills on a torus. We explain this correspondence using the recent results on the equivalence of the…
This review talk focusses on some of the interesting developments in the area of superstring compactification that have occurred in the last couple of years. These include the discovery that ``mirror symmetric" pairs of Calabi--Yau spaces,…
We construct more dual pairs of type II-heterotic strings in four dimensions with $N=2,1$ spacetime supersymmetry. On the type II side the construction utilizes the various possible choices of K3 automorphisms with fixed points which…
We consider the Topological String/Spectral theory duality on toric Calabi-Yau threefolds obtained from the resolution of the cone over the $Y^{N,0}$ singularity. Assuming Kyiv formula, we demonstrate this duality in a special regime thanks…
For a one-parameter family of Calabi-Yau d-fold M embedded in ${{CP}^{d+1}}$, we consider a new quasi-topological field theory ${A^{\ast}}$(M)-model compared with the $A$(M)-model. The two point correlators on the sigma model moduli space…
We introduce a homology theory whose Euler characteristics counts ASD bundles over four dimensional co-associative submanifolds in (almost) G_2 manifolds. As a TQFT, in relative situations, we have the Fukaya-Floer category of Lagrangians…
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 study the resurgent structure of the refined topological string partition function on a non-compact Calabi-Yau threefold, at large orders in the string coupling constant $g_s$ and fixed refinement parameter $\mathsf{b}$. For…
In this article we continue our study of chiral fermions on a quantum curve. This system is embedded in string theory as an I-brane configuration, which consists of D4 and D6-branes intersecting along a holomorphic curve in a complex…