Flat coordinates for Saito Frobenius manifolds and string theory

A. A. Belavin, Doron Gepner, Ya. A. Kononov

Research output: Contribution to journalArticlepeer-review


We investigate the connection between the models of topological conformal theory and noncritical string theory with Saito Frobenius manifolds. For this, we propose a new direct way to calculate the flat coordinates using the integral representation for solutions of the Gauss-Manin system connected with a given Saito Frobenius manifold. We present explicit calculations in the case of a singularity of type A (n) . We also discuss a possible generalization of our proposed approach to SU(N) (k) /(SU(N) (k+1) x U(1)) Kazama-Suzuki theories. We prove a theorem that the potential connected with these models is an isolated singularity, which is a condition for the Frobenius manifold structure to emerge on its deformation manifold. This fact allows using the Dijkgraaf-Verlinde-Verlinde approach to solve similar Kazama-Suzuki models.
Original languageEnglish
Pages (from-to)1775-1789
Number of pages15
JournalTheoretical and Mathematical Physics(Russian Federation)
Issue number3
StatePublished - Dec 2016


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