2D String Theory Coupled to Quantum Gravity

TL;DR

This paper calculates the exact partition function for 2D open strings coupled to quantum gravity, evaluates the string susceptibility, and explores exactly solvable modifications of the Nambu-Goto action on random surfaces.

Contribution

It provides an exact calculation of the partition function and string susceptibility for 2D open strings on random surfaces, including solvable modifications of the Nambu-Goto action.

Findings

Partition function calculated exactly for the model.

String susceptibility for the disk is -1/2.

Certain modifications of the Nambu-Goto action are also exactly solvable.

Abstract

We consider self-avoiding Nambu-Goto open strings on a random surface. We have shown that the partition function of such a string theory can be calculated exactly. The string susceptibility for the disk is evaluated to be $-\frac{1}{2}$. We also consider modifications of the Nambu-Goto action which are exactly soluble on a random surface.