2d Gravity Coupled to Topological Minimal Models

TL;DR

This paper explores the structure of the large phase space in genus-0 topological minimal models coupled to 2d gravity, deriving identities and expressing couplings in terms of flat coordinates, linking large and small phase spaces.

Contribution

It introduces a comprehensive analysis of the large phase space, deriving identities and expressing gravitational couplings via flat coordinates, connecting matter and gravity sectors.

Findings

Derived general identities valid on the large phase space.

Obtained puncture and dilaton equations as special cases.

Expressed gravitational couplings in terms of flat coordinates.

Abstract

We discuss the properties of the large phase space of the genus-0 topological minimal $A_{k + 1}$ model coupled to 2d topological gravity. The minimal action is perturbed by adding all possible gravitational descendants with non-trivial couplings which form the infinite-dimensional large phase space. Some general identities (valid on the large phase space) are derived and the puncture and the dilaton equations are obtained as special cases of these results. Finally we show how the couplings to the gravitational descendants can actually be expressed in terms of the flat coordinates defining the small phase space of the theory. Thus eventually the large phase space becomes determined solely by the LG superpotential characterising the matter sector of the coupled model.