Geodesic
Flat coordinates for Saito Frobenius manifolds and string theory.
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 3, pp. 429-445

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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 $SU(N)_k/(SU(N)_{k+1} \times U(1))$ 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.
Keywords: Frobenius manifold, flat coordinates, string theory. 
@article{TMF_2016_189_3_a8,
     author = {A. A. Belavin and D. Gepner and Ya. A. Kononov},
     title = {Flat coordinates for {Saito} {Frobenius} manifolds and string theory.},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {429--445},
     publisher = {mathdoc},
     volume = {189},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_189_3_a8/}
}
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A. A. Belavin; D. Gepner; Ya. A. Kononov. Flat coordinates for Saito Frobenius manifolds and string theory.. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 3, pp. 429-445. http://geodesic.mathdoc.fr/item/TMF_2016_189_3_a8/