QCD Quark Condensate from SUSY and the Orientifold Large-N Expansion

TL;DR

The paper addresses computing the quark condensate in one-flavor massless QCD by relating it to the exact gluino condensate in ${\cal N}=1$ SYM via orientifold planar equivalence. It develops renormalization-group-invariant formulations and a Lambda parameter that scales smoothly with $1/N$, derives a closed expression for the condensate, and performs numerical estimates that agree with GMOR-based and lattice results. This work demonstrates a novel quantitative application of large-$N$ methods to non-supersymmetric QCD and suggests extensions to subleading $1/N$ corrections and higher-supersymmetry theories. It provides a promising bridge between exact SUSY results and phenomenology of real-world QCD.

Abstract

We estimate the quark condensate in one-flavor massless QCD from the known value of the gluino condensate in SUSY Yang-Mills theory using our newly proposed "orientifold" large-N expansion. The numerical result for the quark condensate renormalized at the scale 2 GeV is then given as a function of alpha_s(2 GeV) and of possible corrections from sub-leading terms. Our value can be compared with the quark condensate in (quenched) lattice QCD or with the one extracted from the Gell-Mann--Oakes--Renner relation by virtue of non-lattice determinations of the quark masses. In both cases we find quite a remarkable agreement.