  Integrability of equations of topological-antitopological fusion (being
proposed by Cecotti and Vafa) describing ground state metric on given 2D
topological field theory (TFT) model, is proved. For massive TFT models these
equations are reduced to a universal form (being independent on the given TFT
model) by gauge transformations. For massive perturbations of topological
conformal field theory models the separatrix solutions of the equations bounded
at infinity are found by the isomonodromy deformations method. Also it is shown
that ground state metric together with some part of the underlined TFT
structure can be parametrized by pluriharmonic maps of the coupling space to
the symmetric space of real positive definite quadratic forms.
