QCD Strings as Constrained Grassmannian Sigma Model:

TL;DR

This paper explores the effective action of string world sheets in three and four dimensions through a correspondence with the constrained Grassmannian sigma model, revealing a Coulomb gas representation with a mass gap.

Contribution

It introduces a novel approach linking string world sheet dynamics to a constrained Grassmannian sigma model, enabling effective action calculations with instanton backgrounds.

Findings

Effective action expressed as a Coulomb gas partition function.

Identification of a dynamically generated mass gap.

Application to N-string interactions at the tree level.

Abstract

We present calculations for the effective action of string world sheet in R3 and R4 utilizing its correspondence with the constrained Grassmannian sigma model. Minimal surfaces describe the dynamics of open strings while harmonic surfaces describe that of closed strings. The one-loop effective action for these are calculated with instanton and anti-instanton background, reprsenting N-string interactions at the tree level. The effective action is found to be the partition function of a classical modified Coulomb gas in the confining phase, with a dynamically generated mass gap.