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Flat coordinates for Saito Frobenius manifolds and string theory. (English. Russian original) Zbl 1358.81147

Theor. Math. Phys. 189, No. 3, 1775-1789 (2016); translation from Teor. Mat. Fiz. 189, No. 3, 429-445 (2016).
Summary: 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 \(\mathrm{SU}(N)_k/(\mathrm{SU}(N)_{k+1} \times \mathrm{U}(1))\) 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.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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References:

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