An Exact Solution to O(26) Sigma Model coupled to 2-D Gravity

TL;DR

This paper provides an exact solution to the O(26) sigma model coupled to 2-D quantum gravity by mapping it to bosonic string theory, including gravitational dressing and beta functions, advancing understanding of 2-D quantum gravity models.

Contribution

It introduces an exact solution to the O(26) sigma model coupled to 2-D gravity, detailing gravitational dressing and modified beta functions, which was not previously available.

Findings

Exact gravitational dressing of matter operators obtained.

Explicit form of gravitationally modified beta function derived.

Discussion on relation to previous asymptotic solutions included.

Abstract

By a mapping to the bosonic string theory, we present an exact solution to the O(26) sigma model coupled to 2-D quantum gravity. In particular, we obtain the exact gravitational dressing to the various matter operators classified by the irreducible representations of O(26). We also derive the exact form of the gravitationally modified beta function for the original coupling constant $e^2$. The relation between our exact solution and the asymptotic solution given in ref[3] is discussed in various aspects.