Topological Two-Dimensional Gravity on Surfaces with Boundary

TL;DR

This paper extends the solution of two-dimensional gravity to surfaces with boundaries, incorporating boundary operators and linking the theory to an extended integrable hierarchy.

Contribution

It generalizes the known bulk theory solution to include boundaries and boundary operators, enabling linearization of Virasoro constraints via an extended KdV hierarchy.

Findings

Solution of 2D gravity on surfaces with boundary using contact interactions.

Inclusion of boundary operators to extend the algebraic structure.

Linearization of Virasoro constraints through an extended integrable hierarchy.

Abstract

We solve two-dimensional gravity on surfaces with boundary in terms of contact interactions and surface degenerations. The known solution of the bulk theory in terms of a contact algebra is generalized to include boundaries and an enlarged set of boundary operators. The latter allow for a linearization of the Virasoro constraints in terms of an extended integrable KdV hierarchy.