Anomaly matching for the QCD string

TL;DR

This paper proposes a criterion based on the trace anomaly of the QCD stress tensor, linking instantons and asymptotic freedom, to evaluate string theory models of QCD, with promising results for SU(2).

Contribution

It introduces a novel anomaly-based criterion for QCD string theories, connecting instanton effects and asymptotic freedom, and demonstrates numerical agreement in a bosonic string model for SU(2).

Findings

Criterion derived from trace anomaly matches numerical results for SU(2).

The approach links instantons and asymptotic freedom in QCD string models.

Formal bosonic string treatment shows promising agreement with QCD properties.

Abstract

A criterion to be satisfied by a string theory of QCD is formulated in the ultraviolet regime. It arises from the trace anomaly of the QCD stress tensor computed using instantons. It is sensitive to asymptotic freedom. It appears to be related to the trace anomaly of the QCD string. Our current understanding of noncritical strings in physical dimensions is limited, but remarkably, a formal treatment of the bosonic string yields numerical agreement both in magnitude and sign for the gauge group SU(2).