Home
| VOLUME 103 (2016) | ISSUE 3 | PAGE 168 |
|---|
|
Flat coordinates of topological CFT and solutions of Gauss-Manin system
A. Belavin+*×, D. Gepner°, Ya. Kononov+∇
+Landau Institute for Theoretical Physics of the RAS, 142432 Chernogolovka, Russia *Institute for Information Transmission Problems of the RAS (Kharkevich Institute), 127051 Moscow, Russia ×Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia °Department of Particle Physics, Weizmann Institute, 7610001 Rehovot, Israel ∇Math Department, Higher School of Economics, National Research University, 117312 Moscow, Russia
Abstract
It was shown many years ago by Dijkgraaf, Velinde, Verlinde for 2d Topological Conformal Field Theory (TCFT) and more recently for the non-critical String theory that some models of these two types can be solved using their connection with the special case of Frobenius Manifolds (FM) so called Saito Frobenius manifolds connected with a deformed singularity. The crucial point for obtaining an explicit expression for the correlators is finding the flat coordinates of SFMs as functions of the parameters of the deformed singularity. We suggest a direct way to find the flat coordinates, using the integral representation for the solutions of Gauss-Manin system connected with the corresponding SFM for the singularity. |