| Preprint | |
| Report number | arXiv:2304.11027 ; CERN-TH-2023-060 |
| Title | Connecting topological strings and spectral theory via non-autonomous Toda equations |
| Author(s) | Gavrylenko, Pavlo (Geneva U. ; SISSA, Trieste ; BITP, Kiev) ; Grassi, Alba (Geneva U. ; CERN) ; Hao, Qianyu (Geneva U.) |
| Imprint | 2023-04-21 |
| Number of pages | 68 |
| Note | 68 pages. v2: references and some technical details added |
| Subject category | math.SP ; Mathematical Physics and Mathematics ; math.MP ; Mathematical Physics and Mathematics ; math-ph ; Mathematical Physics and Mathematics ; hep-th ; Particle Physics - Theory |
| Abstract | 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$$SU(N)$ super Yang-Mills. |
| Other source | Inspire |
| Copyright/License | preprint: (License: arXiv nonexclusive-distrib 1.0) |
Notice créée le 2023-04-25, modifiée le 2024-03-20