The quantum tropical vertex

Bousseau, Pierrick

doi:10.2140/gt.2020.24.1297

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

This article is available for purchase or by subscription. See below.

The quantum tropical vertex

Pierrick Bousseau

Geometry & Topology 24 (2020) 1297–1379

DOI: 10.2140/gt.2020.24.1297

Abstract

Gross, Pandharipande and Siebert have shown that the $2$ –dimensional Kontsevich–Soibelman scattering diagrams compute certain genus-zero log Gromov–Witten invariants of log Calabi–Yau surfaces. We show that the $q$ –refined $2$ –dimensional Kontsevich–Soibelman scattering diagrams compute, after the change of variables $q = e^{i ℏ}$ , generating series of certain higher-genus log Gromov–Witten invariants of log Calabi–Yau surfaces.

This result provides a mathematically rigorous realization of the physical derivation of the refined wall-crossing formula from topological string theory proposed by Cecotti and Vafa and, in particular, can be viewed as a nontrivial mathematical check of the connection suggested by Witten between higher-genus open A–model and Chern–Simons theory.

We also prove some new BPS integrality results and propose some other BPS integrality conjectures.

PDF Access Denied

We have not been able to recognize your IP address 3.21.106.69 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

scattering diagrams, quantum tori, Gromov–Witten invariants

Mathematical Subject Classification 2010

Primary: 14N35

References

Publication

Received: 15 November 2018

Revised: 1 July 2019

Accepted: 4 September 2019

Published: 30 September 2020

Proposed: Jim Bryan

Seconded: Dan Abramovich, Richard P Thomas

Authors

Pierrick Bousseau
Department of Mathematics Imperial College London London United Kingdom	Institute for Theoretical Studies ETH Zürich Zürich Switzerland

Volume 24, issue 3 (2020)