Confinement without symmetry breaking in chiral gauge theories

Abstract

The infrared structure of gauge theories with chiral fermions remains largely unexplored. In this work we investigate the Bars-Yankielowicz class using the functional renormalisation group, building on recent developments in gauge-fermion systems that provide clear criteria for confinement and dynamical symmetry breaking. We show that two distinct phases arise: one exhibiting both confinement and symmetry breaking at small numbers of colours, and another characterised by confinement without symmetry breaking in the large-colour limit. The latter realises a novel regime, opening the possibility of exotic spectra and phenomena that can now be studied within a systematic framework.

Figures (5)

• Figure 1: Ghost–gauge (left panel), three-gauge (centre panel, solid line), four-gauge (centre panel, dashed line) gauge-$\chi$ (right panel, plain line) and gauge-$\psi$ (right panel, dashed line) exchange couplings for a BY theory with $N_c=3$ (red line), 4 (yellow), 5 (light blue) and 6 (dark blue). While for $N_c \geq 4$, the scaling confining solutions are shown, for $N_c = 3$, $\textrm{d}\textrm{SB}$ occurs, signalled by a singularity in the four-fermion couplings that propagates to the rest of the couplings. In this case, a nearby trajectory to the confining is displayed for illustration purposes.
• Figure 2: Four-fermion couplings, as defined in \ref{['eq:four-fermioneff']}, for $N_c=3$ (red line), 4 (yellow), 5 (light blue) and 6 (dark blue) BY theories.
• Figure 3: $\alpha^\textrm{crit}_{\textrm{SB}}$ (green line) and the maximum value of the gauge-$\chi$ exchange coupling (blue line) as a function of $N_c$. As shaded blue region the estimated uncertainty in the minimisation of the STI. The vertical dashed line marks $N_c^{\rm crit}$ in \ref{['eq:Nccrit']}.
• Figure 4: Gauge (left) and ghost (centre) field wave functions and the $\chi$-gauge exchange coupling (right) in a $N_c=5$ BY theory with different onsets of the power-law scaling in the flow of the mass gap. From darker blue to green the onset (given by the deviation from the logarithmic scaling) is delayed between to limiting scenarios as marked by the gray vertical shaded area. The horizontal shaded area in the right-most plot shows the error estimate in the peak of the gauge-fermion strength.
• Figure 5: On the top, we show the value of the gauge field two point function in the deep IR as a function of the value of the mass gap in the UV. On the bottom row, we show the gauge (left) and ghost (centre) wave function and the ghost-gauge exchange coupling (right) for a $N_c=5$ BY theory. Different curves correspond to different onsets of the quadratic part of the gauge mass gap with the same colour coding as the top plot. From darker blue to green the onset (given by the deviation from the logarithmic scaling) is delayed.