scholarly journals Geometric transition in the nonperturbative topological string

2016 ◽  
Vol 94 (5) ◽  
Author(s):  
Yuji Sugimoto
Keyword(s):  
Topological String ◽  
Geometric Transition

scholarly journals Holomorphic anomaly equation for and the Nekrasov-Shatashvili limit of local

2021 ◽  
Vol 9 ◽  
Author(s):  
Pierrick Bousseau ◽  
Honglu Fan ◽  
Shuai Guo ◽  
Longting Wu
Keyword(s):  
Elliptic Curve ◽  
Moduli Spaces ◽  
Topological String ◽  
Holomorphic Anomaly ◽  
Holomorphic Anomaly Equation ◽  
Anomaly Equation ◽  
Witten Theory ◽  
Generating Series ◽  
Maximal Contact ◽  
Higher Genus

Abstract We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X,D)$ a pair with X a smooth projective variety and D a nef smooth divisor, maximal contact Gromov-Witten theory of $(X,D)$ with $\lambda _g$ -insertion is related to Gromov-Witten theory of the total space of ${\mathcal O}_X(-D)$ and local Gromov-Witten theory of D. Specializing to $(X,D)=(S,E)$ for S a del Pezzo surface or a rational elliptic surface and E a smooth anticanonical divisor, we show that maximal contact Gromov-Witten theory of $(S,E)$ is determined by the Gromov-Witten theory of the Calabi-Yau 3-fold ${\mathcal O}_S(-E)$ and the stationary Gromov-Witten theory of the elliptic curve E. Specializing further to $S={\mathbb P}^2$ , we prove that higher genus generating series of maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ are quasimodular and satisfy a holomorphic anomaly equation. The proof combines the quasimodularity results and the holomorphic anomaly equations previously known for local ${\mathbb P}^2$ and the elliptic curve. Furthermore, using the connection between maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ and Betti numbers of moduli spaces of semistable one-dimensional sheaves on ${\mathbb P}^2$ , we obtain a proof of the quasimodularity and holomorphic anomaly equation predicted in the physics literature for the refined topological string free energy of local ${\mathbb P}^2$ in the Nekrasov-Shatashvili limit.

scholarly journals BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations

2021 ◽  
Author(s):  
Giulio Bonelli ◽  
Fabrizio Del Monte ◽  
Alessandro Tanzini
Keyword(s):  
Topological String ◽  
Cluster Algebra ◽  
Painlevé Equations ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Particle Spectrum ◽  
Yang Mills ◽  
Painleve Equations ◽  
Rank One ◽  
Bilinear Equations

AbstractWe study the discrete flows generated by the symmetry group of the BPS quivers for Calabi–Yau geometries describing five-dimensional superconformal quantum field theories on a circle. These flows naturally describe the BPS particle spectrum of such theories and at the same time generate bilinear equations of q-difference type which, in the rank one case, are q-Painlevé equations. The solutions of these equations are shown to be given by grand canonical topological string partition functions which we identify with $$\tau $$ τ -functions of the cluster algebra associated to the quiver. We exemplify our construction in the case corresponding to five-dimensional SU(2) pure super Yang–Mills and $$N_f=2$$ N f = 2 on a circle.

scholarly journals Topological string correlators from matrix models

2015 ◽  
Vol 2015 (3) ◽  
Author(s):  
Robert de Mello Koch ◽  
Lwazi Nkumane
Keyword(s):  
Matrix Models ◽  
Topological String

scholarly journals Topological string on toric CY3s in large complex structure limit

2009 ◽  
Vol 813 (3) ◽  
pp. 315-348
Author(s):  
Lalla Btissam Drissi ◽  
Houda Jehjouh ◽  
El Hassan Saidi
Keyword(s):  
Complex Structure ◽  
Topological String ◽  
Large Complex ◽  
Large Complex Structure

String theory

2018 ◽  
Author(s):  
Ivan Kostov
Keyword(s):  
String Theory ◽  
Matrix Models ◽  
Topological Strings ◽  
Mirror Symmetry ◽  
Topological String ◽  
Enumerative Geometry ◽  
Topological String Theory ◽  
Superstring Theory ◽  
String Dualities ◽  
Supersymmetric Gauge

This article discusses the link between matrix models and string theory, giving emphasis on topological string theory and the Dijkgraaf–Vafa correspondence, along with applications of this correspondence and its generalizations to supersymmetric gauge theory, enumerative geometry, and mirror symmetry. The article first provides an overview of strings and matrices, noting that the correspondence between matrix models and string theory makes it possible to solve both non-critical strings and topological strings. It then describes some basic aspects of topological strings on Calabi-Yau manifolds and states the Dijkgraaf–Vafa correspondence, focusing on how it is connected to string dualities and how it can be used to compute superpotentials in certain supersymmetric gauge theories. In addition, it shows how the correspondence extends to toric manifolds and leads to a matrix model approach to enumerative geometry. Finally, it reviews matrix quantum mechanics and its applications in superstring theory.

scholarly journals Geometric transition in friction for flow over a bubble mattress

2009 ◽  
Vol 21 (1) ◽  
pp. 011701 ◽  
Author(s):  
Anthony M. J. Davis ◽  
Eric Lauga
Keyword(s):  
Geometric Transition
Sign in / Sign up

Export Citation Format

Share Document