Lattice Study of Planar Equivalence: The Quark Condensate

TL;DR

This study investigates whether different fermion representations in SU(N) gauge theories become equivalent at large N, using lattice simulations of the quark condensate across various SU(N) groups.

Contribution

It provides non-perturbative evidence supporting planar equivalence in SU(N) gauge theories with different fermion representations through lattice simulations.

Findings

Data supports non-perturbative equivalence at large N

Subleading corrections are discussed

Quenched lattice results align with theoretical predictions

Abstract

We study quenched SU(N) gauge theories with fermions in the two-index symmetric, antisymmetric and the adjoint representations. Our main motivation is to check whether at large number of colours those theories become non-perturbatively equivalent. We prove the equivalence assuming that the charge-conjugation symmetry is not broken in pure Yang-Mills theory. We then carry out a quenched lattice simulation of the quark condensate in the symmetric, antisymmetric and the adjoint representations for SU(2), SU(3), SU(4), SU(6) and SU(8). We show that the data support the equivalence and discuss the size of subleading corrections.