Orientifold Planar Equivalence: The Chiral Condensate

TL;DR

This paper proves the orientifold planar equivalence for chiral condensates in large N SU(N) gauge theories, supports it with numerical data up to N=8, and discusses implications for unquenched theories.

Contribution

It provides a lattice proof of the equivalence for quenched condensates and numerical evidence supporting the large N predictions.

Findings

Numerical condensate data up to N=8 supports the equivalence.

Subleading 1/N corrections are significant at N=3.

The proof assumes charge conjugation invariance in the large N limit.

Abstract

The recently introduced orientifold planar equivalence is a promising tool for solving non-perturbative problems in QCD. One of the predictions of orientifold planar equivalence is that the chiral condensates of a theory with $N_f$ flavours of Dirac fermions in the symmetric (or antisymmetric) representation and $N_f$ flavours of Majorana fermions in the adjoint representation have the same large $N$ value for any value of the mass of the (degenerate) fermions. Assuming the invariance of the theory under charge conjugation, we prove this statement on the lattice for staggered quenched condensates in SU($N$) Yang-Mills in the large $N$ limit. Then, we compute numerically those quenched condensates for $N$ up to 8. After separating the even from the odd corrections in $1/N$, we are able to show that our data support the equivalence; however, unlike other quenched observables, subleading terms in $1/N$ are needed for describing the data for the symmetric and antisymmetric representation at $N$=3. Possible lessons for the unquenched case are discussed.