"Hodge strings" and elements of K.Saito's theory of the Primitive form

Details "Hodge strings" and elements of K.Saito's theory of the Primitive form "Hodge strings" and elements of K.Saito's theory of the Primitive form

1998-01-27

arxiv.org/abs/hep-th/9801179v1

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 32pp

Scientific paper

The "Hodge strings" construction of solutions to associativity equations is proposed. From the topological string theory point of view this construction formalizes the "integration over the position of the marked point" procedure for computation of amplitudes. From the mathematical point of view the "Hodge strings" construction is just a composition of elements of harmonic theory (known among physicists as a $t$-part of $t-t^*$ equations) and the K.Saito construction of flat coordinates (starting from flat connection with a spectral parameter). We also show how elements of K.Saito theory of primitive form appear naturally in the "Landau-Ginzburg" version of harmonic theory if we consider the holomorphic pieces of germs of harmonic forms at the singularity.

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