Topological Recursion and Uncoupled BPS Structures II: Voros Symbols and the τ-Function

We continue our study of the correspondence between BPS structures and topological recursion in the uncoupled case, this time from the viewpoint of quantum curves. For spectral curves of hypergeometric type, we show the Borel-resummed Voros symbols of the corresponding quantum curves solve Bridgelan...

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Veröffentlicht in:Communications in mathematical physics Jg. 399; H. 1; S. 519 - 572
Hauptverfasser: Iwaki, Kohei, Kidwai, Omar
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2023
Springer Nature B.V
Schlagworte:
Classical and Quantum Gravitation
Complex Systems
Fourier transforms
Mathematical and Computational Physics
Mathematical Physics
Parameters
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Symbols
Theoretical
Topology
ISSN:0010-3616, 1432-0916
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Zusammenfassung:We continue our study of the correspondence between BPS structures and topological recursion in the uncoupled case, this time from the viewpoint of quantum curves. For spectral curves of hypergeometric type, we show the Borel-resummed Voros symbols of the corresponding quantum curves solve Bridgeland’s “BPS Riemann–Hilbert problem”. In particular, they satisfy the required jump property in agreement with the generalized definition of BPS indices Ω in our previous work. Furthermore, we observe the Voros coefficients define a closed one-form on the parameter space, and show that (log of) Bridgeland’s τ -function encoding the solution is none other than the corresponding potential, up to a constant. When the quantization parameter is set to a special value, this agrees with the Borel sum of the topological recursion partition function Z TR , up to a simple factor.
Bibliographie:ObjectType-Article-1
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ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-022-04563-y