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Статья

Flat coordinates for Saito Frobenius manifolds and string theory

Theoretical and Mathematical Physics. 2016. Vol. 189. No. 3. P. 1775-1789.
Belavin A., Gepner D., Kononov Y.

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 An. We also discuss a possible generalization of our proposed approach to SU(N)k/(SU(N)k+1 × 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.