Quantum curves from refined topological recursion: The genus 0 case

Kidwai, Omar; Osuga, Kento

doi:10.1016/j.aim.2023.109253

Advances in Mathematics

2023

DOI: 10.1016/j.aim.2023.109253

|View full text |Cite

Quantum curves from refined topological recursion: The genus 0 case

Omar Kidwai,

Kento Osuga

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 73 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Deformation and Quantisation Condition of the $$\mathcal {Q}$$-Top Recursion

Osuga

2024

Ann. Henri Poincaré

View full text Add to dashboard Cite

We consider a deformation of a family of hyperelliptic refined spectral curves and investigate how deformation effects appear in the hyperelliptic refined topological recursion as well as the $$\mathcal {Q}$$ Q -top recursion. We then show a coincidence between a deformation condition and a quantisation condition in terms of the $$\mathcal {Q}$$ Q -top recursion on a degenerate elliptic curve. We also discuss a relation to the corresponding Nekrasov–Shatashivili effective twisted superpotential.

show abstract

Deformation and Quantisation Condition of the $$\mathcal {Q}$$-Top Recursion

Osuga

2024

Ann. Henri Poincaré

View full text Add to dashboard Cite

show abstract

Refined Topological Recursion Revisited: Properties and Conjectures

Osuga

2024

Commun. Math. Phys.

View full text Add to dashboard Cite

For any (possibly singular) hyperelliptic curve, we give the definition of a hyperelliptic refined spectral curve and the hyperelliptic refined topological recursion, generalising the formulation for a special class of genus-zero curves by Kidwai and the author, and also improving the proposal by Chekhov and Eynard. Along the way, we uncover a fundamental geometric structure underlying the hyperelliptic refined topological recursion and investigate its properties — parts of which remain conjectural due to computational difficulties. Moreover, we establish a new recursion valid in the so-called Nekrasov-Shatashivili limit and prove existence of the corresponding quantum curve.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Quantum curves from refined topological recursion: The genus 0 case

Cited by 2 publications

References 73 publications

Deformation and Quantisation Condition of the $$\mathcal {Q}$$-Top Recursion

Deformation and Quantisation Condition of the $$\mathcal {Q}$$-Top Recursion

Refined Topological Recursion Revisited: Properties and Conjectures

Contact Info

Product

Resources

About