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Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
by Thomas T. Dumitrescu, Po-Shen Hsin
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Submission summary
| Authors (as registered SciPost users): | Thomas Dumitrescu · Po-Shen Hsin |
| Submission information | |
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| Preprint Link: | scipost_202408_00034v1 (pdf) |
| Date accepted: | 2024-09-10 |
| Date submitted: | 2024-08-30 18:36 |
| Submitted by: | Hsin, Po-Shen |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In gauge theories with fundamental matter there is typically no sharp way to distinguish confining and Higgs regimes, e.g. using generalized global symmetries acting on loop order parameters. It is standard lore that these two regimes are continuously connected, as has been explicitly demonstrated in certain lattice and continuum models. We point out that Higgsing and confinement sometimes lead to distinct symmetry protected topological (SPT) phases -- necessarily separated by a phase transition -- for ordinary global symmetries. We present explicit examples in 3+1 dimensions, obtained by adding elementary Higgs fields and Yukawa couplings to QCD while preserving parity P and time reversal T. In a suitable scheme, the confining phases of these theories are trivial SPTs, while their Higgs phases are characterized by non-trivial P- and T-invariant theta-angles $\theta_f, \theta_g = \pi$ for flavor or gravity background gauge fields, i.e. they are topological insulators or superconductors. Finally, we consider conventional three-flavor QCD (without elementary Higgs fields) at finite $U(1)_B$ baryon-number chemical potential $\mu_B$, which preserves P and T. At very large $\mu_B$, three-flavor QCD is known to be a completely Higgsed color superconductor that also spontaneously breaks $U(1)_B$. We argue that this high-density phase is in fact a gapless SPT, with a gravitational theta-angle $\theta_g = \pi$ that safely co-exists with the $U(1)_B$ Nambu-Goldstone boson. We explain why this SPT motivates unexpected transitions in the QCD phase diagram, as well as anomalous surface modes at the boundary of quark-matter cores inside neutron stars.
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Author comments upon resubmission
List of changes
- On p20 to account for the second referee report, we add a new footnote 48 to mention the experiment bound by 10^{-10} on the T symmetry breaking in QCD and cite the latest Particle Data Group review in 2024.
Note the main text already extensively discussed the consequence for the case of broken T throughout all sections.
- On p42 to account for the second referee report, around (2.55) we add a new footnote 67 to clarify the 't Hooft anomalies.
- On p49 to account for the second referee report, above (4.9) we added a few words that by introducing the fundamental Higgs field, (-1)F is no longer identified with the center of gauge group and thus the gauge group can be completely broken
- On p67 to account for the second referee report, near (6.4) we add a new footnote 97 to reiterate the condition stated in the beginning in section 6.1 that we take the chemical potential to be much larger than the quark mass
Published as SciPost Phys. 17, 093 (2024)