SUSY Relics in One-Flavor QCD from a New 1/N Expansion

TL;DR

This paper introduces a novel large-N_c expansion for multi-flavor QCD that links to supersymmetric theories, providing new insights and testable predictions for N_f=1 QCD and potential applications to real-world QCD.

Contribution

It proposes a new 1/N_c expansion for multi-flavor QCD based on an equivalence in SU(3), connecting non-supersymmetric QCD to supersymmetric gluodynamics for N_f=1.

Findings

Derived qualitative predictions for N_f=1 QCD.

Established equivalence between N=1 supersymmetric gluodynamics and a specific large-N_c limit.

Suggested testable lattice simulation predictions.

Abstract

We suggest a new large-N_c limit for multi flavor QCD. Since fundamental and two-index antisymmetric representations are equivalent in SU(3), we have the option to define SU(N_c) QCD keeping quarks in the latter. We can then define a new 1/N_c expansion (at fixed number of flavors N_f) that shares appealing properties with the topological (fixed N_f/N_c) expansion while being more suitable for theoretical analysis. In particular, for N_f=1, our large-N_c limit gives a theory that we recently proved to be equivalent, in the bosonic sector, to N=1 supersymmetric gluodynamics. Using known properties of the latter, we derive several qualitative and semi-quantitative predictions for N_f=1 massless QCD which can be easily tested in lattice simulations. Finally, we comment on possible applications for pure SU(3) Yang-Mills theory and real QCD.