Chiral properties of SU(3) sextet fermions

TL;DR

This paper investigates the chiral symmetry breaking patterns in SU(3) gauge theory with sextet fermions, confirming expectations through lattice simulations and random matrix theory comparisons.

Contribution

It provides the first detailed analysis of chiral properties of sextet fermions, verifying symmetry breaking patterns and zero mode behavior with lattice and random matrix models.

Findings

Zero mode counts increase fivefold compared to fundamental

Random matrix ensembles describe Dirac eigenvalues well

Zero modes not always linked to integer topological charge

Abstract

SU(3) gauge theory with overlap fermions in the 2-index symmetric (sextet) and fundamental representations is considered. A priori it is not known what the pattern of chiral symmetry breaking is in a higher dimensional representation although the general expectation is that if two representations are both complex, the breaking pattern will be the same. This expectation is verified for the sextet at N_f = 0 in several exact zero mode sectors. It is shown that if the volume is large enough the same random matrix ensemble describes both the sextet and fundamental Dirac eigenvalues. The number of zero modes for the sextet increases approximately 5-fold relative to the fundamental in accordance with the index theorem for small lattice spacing but zero modes which do not correspond to integer topological charge do exist at larger lattice spacings. The zero mode number dependence of the random matrix model predictions correctly match the simulations in each sector and each representation.