Mass hierarchies in gauge theory with two index symmetric representation matter

TL;DR

This paper uses a holographic model to predict large mass hierarchies in gauge theories with two index symmetric and fundamental fermions, showing how scale separation varies with parameters and quark mass.

Contribution

It introduces a holographic approach to estimate mass hierarchies in SU(Nc) gauge theories with mixed fermion representations, extending understanding of scale separation in these models.

Findings

Maximum hierarchy factor of 13 for Nc=7, NfF=22

Hierarchy can exceed 7 for various Nc by tuning NfF

Distinct mass gaps are achievable even with perturbative gamma extrapolation

Abstract

In gauge theories, the running of the anomalous dimension of a fermion bilinear operator is believed to lead to chiral symmetry breaking when gamma=1. Naively using perturbative results to judge when gamma=1 leads to the possibility of large dynamically generated mass hierarchies in models with both two index symmetric representation and fundamental representation fermions. In this paper we study a holographic model of this physics to predict the separation in scales in the meson spectrum. We study SU(Nc) theories at different Nc with one flavour of two index symmetric representation as a function of the number of fundamental fermion flavours NfF. The largest hierarchy we find is for Nc=7 and NfF=22 where the rho mesons made of the two different representations are separated in scale by a factor of 13. For general Nc the hierarchy can be made greater than 7 by tuning NfF. We display the hierarchy as a function of NfF and investigate the quark mass dependence. These predictions do depend on the extrapolation of gamma from the perturbative regime - even in a pessimistic scenario a distinct gap can be achieved.