SwissMAP Logo
Log in
  • About us
    • Organization
    • Professors
    • Senior Researchers
    • Postdocs
    • PhD Students
    • Alumni
  • News & Events
    • News
    • Events
    • Online Events
    • Videos
    • Newsletters
    • Press Coverage
    • Perspectives Journal
    • Interviews
  • Research
    • Basic Notions
    • Phase III Directions
    • Phases I & II Projects
    • Publications
    • SwissMAP Research Station
  • Awards, Visitors & Vacancies
    • Awards
    • Innovator Prize
    • Visitors
    • Vacancies
  • Outreach & Education
    • Masterclasses & Doctoral Schools
    • Mathscope
    • Maths Club
    • Athena Project
    • ETH Math Youth Academy
    • SPRING
    • Junior Euler Society
    • General Relativity for High School Students
    • Outreach Resources
    • Exhibitions
    • Previous Programs
    • Events in Outreach
    • News in Outreach
  • Equal Opportunities
    • Mentoring Program
    • Financial Support
    • SwissMAP Scholars
    • Events in Equal Opportunities
    • News in Equal Opportunities
  • Contact
    • Corporate Design
  • Basic Notions
  • Phase III Directions
  • Phases I & II Projects
  • Publications
  • SwissMAP Research Station

Connecting topological strings and spectral theory via non-autonomous Toda equations

Pavlo Gavrylenko, Alba Grassi, Qianyu Hao

21/4/23 Published in : arXiv:2304.11027

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 to an underlying connection between spectral determinants of quantum mirror curves and the non-autonomous (q)-Toda system. We further exploit this link to connect small and large time expansions in Toda equations. In particular we provide an explicit expression for their tau functions at large time in terms of a strong coupling version of irregular W_N conformal blocks at c=N-1. These are related to a special class of multi-cut matrix models which describe the strong coupling regime of four dimensional, \mathcal{N}=2 super Yang-Mills.

Entire article

Phase I & II research project(s)

  • String Theory
  • Field Theory
  • Geometry, Topology and Physics

Phase III direction(s)

  • Holography and bulk-boundary correspondence
  • From Field Theory to Geometry and Topology

Unlimited One-Way Steering

Newspaper Story Problems and Other Tasks for Context Based Physics Education: A Research Based report on classroom practice

  • Leading house

  • Co-leading house


The National Centres of Competence in Research (NCCRs) are a funding scheme of the Swiss National Science Foundation

© SwissMAP 2025 - All rights reserved