Geometry and Integrability of Topological-Antitopological Fusion

TL;DR

This paper proves the integrability of topological-antitopological fusion equations in 2D TFT models, showing their universal form and solutions via isomonodromy deformations, and relates the ground state metric to pluriharmonic maps.

Contribution

It establishes the integrability of the fusion equations, reduces them to a universal form, and connects the ground state metric to pluriharmonic maps, advancing understanding of 2D TFT models.

Findings

Integrability of fusion equations is proven.

Universal form of equations for massive TFT models is derived.

Solutions for massive perturbations are obtained using isomonodromy deformations.

Abstract

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.