Related papers: Topological String Partition Functions as Polynomi…
We review the polynomial structure of the topological string partition functions as solutions to the holomorphic anomaly equations. We also explain the connection between the ring of propagators defined from special K\"ahler geometry and…
We propose a non-perturbative definition for refined topological strings. This can be used to compute the partition function of superconformal theories in 5 dimensions on squashed S^5 and the superconformal index of a large number of 6…
We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli…
We study mass-deformed N=2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)-brane webs in type II string theory using Nekrasov's instanton calculus, secondly,…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
In this paper we describe an approach to construct semiclassical partition functions in gravity which are complete in the sense that they contain a complete description of the differentiable structures of the underlying 4-manifold. In…
Important illustration to the principle ``partition functions in string theory are $\tau$-functions of integrable equations'' is the fact that the (dual) partition functions of $4d$ $\mathcal{N}=2$ gauge theories solve Painlev\'e equations.…
We study topological string amplitudes for the local half K3 surface. We develop a method of computing higher-genus amplitudes along the lines of the direct integration formalism, making full use of the Seiberg-Witten curve expressed in…
In this work we define a unified generating functions for 9 different kinds of set partitions including cyclically ordered set partitions. Such generating function depends on 4 parameters. We consider property of this function and provide…
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…
We show how to make a topological string theory starting from an $N=4$ superconformal theory. The critical dimension for this theory is $\hat c= 2$ ($c=6$). It is shown that superstrings (in both the RNS and GS formulations) and critical…
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…
We show that certain type II string amplitudes at genus $g$ are given by the topological partition function $F_g$ discussed recently by Bershadsky, Cecotti, Ooguri and Vafa. These amplitudes give rise to a term in the four-dimensional…
For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…
Perturbative string amplitudes are correctly derived from the string geometry theory, which is one of the candidates of a non-perturbative formulation of string theory. In order to derive non-perturbative effects rather easily, we formulate…
We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
A conjecture for computing all genus topological closed string amplitudes on toric local Calabi-Yau threefolds, by interpreting the associated 5-brane web as a Feynman diagram, is given. A propagator and a three point vertex is defined…
This is the text of my habilitation thesis defended at the \'Ecole Normale Sup\'erieure. The topological string presents an arena in which many features of string theory proper, such as the interplay between worldsheet and target space…
We sharpen the duality between open and closed topological string partition functions for topological gravity coupled to matter. The closed string partition function is a generalised Kontsevich matrix model in the large dimension limit. We…