Anomaly matching for the QCD string

It is found possible to formulate a criterion to be satisfied by a string theory of QCD at short distances arising from the trace anomaly of the QCD stress tensor computed using instantons. It is sensitive to asymptotic freedom and 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)