Exotic Non-Supersymmetric Gauge Dynamics from Supersymmetric QCD

TL;DR

This work extends Seiberg's SUSY QCD framework to nonsupersymmetric settings by introducing soft SUSY-breaking terms and analyzes the resulting vacuum structure across different N_f/N_c regimes. By formulating an effective Lagrangian in terms of gauge-invariant composites and employing anomaly matching, the authors uncover exotic vacua with massless composite fermions and, in certain cases, spontaneously broken baryon number, while showing that Seiberg duality can survive small SUSY breaking. They discuss the decoupling limit, where many exotic features disappear as heavy superpartners decouple, and argue that some phenomena may still be observable via lattice simulations with carefully tuned parameters. The study highlights rich nonperturbative dynamics in nonsupersymmetric gauge theories, offering guidance for lattice explorations and potential insights into strong coupling beyond conventional chiral symmetry breaking.

Abstract

We extend Seiberg's qualitative picture of the behavior of supersymmetric QCD to nonsupersymmetric models by adding soft supersymmetry breaking terms. In this way, we recover the standard vacuum of QCD with $N_f$ flavors and $N_c$ colors when $N_f < N_c$. However, for $N_f \geq N_c$, we find new exotic states---new vacua with spontaneously broken baryon number for $N_f = N_c$, and a vacuum state with unbroken chiral symmetry for $N_f > N_c$. These exotic vacua contain massless composite fermions and, in some cases, dynamically generated gauge bosons. In particular Seiberg's electric-magnetic duality seems to persist also in the presence of (small) soft supersymmetry breaking. We argue that certain, specially tailored, lattice simulations may be able to detect the novel phenomena. Most of the exotic behavior does not survive the decoupling limit of large SUSY breaking parameters.

Figures (2)

• Figure 1: The potential $V(t)$ for softly broken supersymmetric Yang-Mills theory with ${N_c} = 3$, ${N_f} = 2$.
• Figure 2: The potential $\Delta V$ for softly broken supersymmetric Yang-Mills theory with ${N_c} = 3$, ${N_f} = 3$. The potential is shown on the subspace $T = t \cdot {\bf 1}$, as a function of $t$. The three curves correspond to $(B_B/B_T) = {1\over 3}, 1, 3$, from bottom to top. The dotted line shows the location of the stationary point (3) referred to in the text.