Chiral symmetry in the weak- and ultra-strong-coupling limits

Determine the fate of chiral symmetry in the strict ultra-strong-coupling limit g\to\infty and in the weak-coupling regime of two-flavor matrix adjoint QC$_2$D, including the effects of emergent flat directions and possible localization-delocalization transitions on the ground-state structure and spectrum.

Background

The analysis establishes the phase structure only in the intermediate-to-strong coupling range, approximately 0.4\lesssim g\lesssim 5, where the variational numerical method converges reliably. The authors note that the strict g\to\infty limit may develop emergent flat directions, while extrapolation toward weak coupling may involve localization-delocalization transitions affecting flavor sectors. Because these phenomena can alter the ground-state structure and spectrum, the fate of chiral symmetry at both coupling extremes is left unresolved and identified as an open question.

References

For larger values of $g$, the qualitative picture is expected to remain more or less the same. Nevertheless, the strict $g \to \infty$ limit requires separate consideration, as emergent flat directions may significantly complicate the ground state structure and the nature of the spectrum. Similarly, the extrapolation to the weak-coupling regime is not straightforward, since localization-delocalization transitions may affect one or more flavor sectors. The fate of chiral symmetry in these regimes remains an important open question and is currently under investigation.

— The fate of chiral symmetry in two-flavor matrix adjoint QC$_2$D  (2608.24064 - Acharyya et al., 25 Aug 2026) in Section 4, Discussion