Minimal String Theory is Logarithmic

TL;DR

This paper demonstrates that minimal string theories, specifically the (p,q) models coupled with 2D gravity, exhibit logarithmic behavior in their four-point tachyon correlation functions, revealing their logarithmic conformal field theory nature.

Contribution

It shows that minimal string theories are logarithmic conformal field theories, expanding understanding of their correlation functions and relation to logarithmic degenerate fields.

Findings

Four-point tachyon correlators have logarithmic singularities.

The theory is identified as a logarithmic conformal field theory.

Results hold for all (p,q) minimal models.

Abstract

We study the simplest examples of minimal string theory whose worldsheet description is the unitary (p,q) minimal model coupled to two-dimensional gravity (Liouville field theory). In the Liouville sector, we show that four-point correlation functions of `tachyons' exhibit logarithmic singularities, and that the theory turns out to be logarithmic. The relation with Zamolodchikov's logarithmic degenerate fields is also discussed. Our result holds for generic values of (p,q).