To Break or Not to Break: A Review of a No-Go Theorem on Chiral Symmetry Breaking in QCD-like Theories
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914027128487936 |
|---|---|
| author | Xu, Ling-Xiao |
| author_facet | Xu, Ling-Xiao |
| contents | This is a pedagogical review of some recent progress in rigorously proving chiral symmetry breaking in a class of QCD-like theories that closely resemble the real-world QCD, namely the $SU(N_c)$ Yang-Mills theory coupled to $N_f$ flavors of massless quarks in the fundamental representation. Based on 't Hooft anomaly matching and persistent mass conditions, a general no-go theorem is formulated: assuming that the theory flows in the infrared to a fully color-screened, infrared-free phase described by color-singlet hadrons, symmetry and anomaly constraints necessarily imply spontaneous chiral symmetry breaking; conversely, any phase with unbroken chiral symmetry must retain unscreened color charges, thereby ruling out a fully color-singlet hadron description in the infrared. While these results have been widely assumed, the recent developments reviewed here establish them with a new level of rigor. The persistent mass condition, carefully formulated here, plays a central role, just as it does in the Vafa-Witten theorem on unbroken vectorlike symmetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06190 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | To Break or Not to Break: A Review of a No-Go Theorem on Chiral Symmetry Breaking in QCD-like Theories Xu, Ling-Xiao High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory This is a pedagogical review of some recent progress in rigorously proving chiral symmetry breaking in a class of QCD-like theories that closely resemble the real-world QCD, namely the $SU(N_c)$ Yang-Mills theory coupled to $N_f$ flavors of massless quarks in the fundamental representation. Based on 't Hooft anomaly matching and persistent mass conditions, a general no-go theorem is formulated: assuming that the theory flows in the infrared to a fully color-screened, infrared-free phase described by color-singlet hadrons, symmetry and anomaly constraints necessarily imply spontaneous chiral symmetry breaking; conversely, any phase with unbroken chiral symmetry must retain unscreened color charges, thereby ruling out a fully color-singlet hadron description in the infrared. While these results have been widely assumed, the recent developments reviewed here establish them with a new level of rigor. The persistent mass condition, carefully formulated here, plays a central role, just as it does in the Vafa-Witten theorem on unbroken vectorlike symmetries. |
| title | To Break or Not to Break: A Review of a No-Go Theorem on Chiral Symmetry Breaking in QCD-like Theories |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.06190 |