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HiggsConfinement Transitions in QCD from Symmetry Protected Topological Phases
by Thomas T. Dumitrescu, PoShen Hsin
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Submission summary
Authors (as registered SciPost users):  Thomas Dumitrescu · PoShen Hsin 
Submission information  

Preprint Link:  scipost_202408_00034v1 (pdf) 
Date accepted:  20240910 
Date submitted:  20240830 18:36 
Submitted by:  Hsin, PoShen 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

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 nontrivial P and Tinvariant thetaangles $\theta_f, \theta_g = \pi$ for flavor or gravity background gauge fields, i.e. they are topological insulators or superconductors. Finally, we consider conventional threeflavor QCD (without elementary Higgs fields) at finite $U(1)_B$ baryonnumber chemical potential $\mu_B$, which preserves P and T. At very large $\mu_B$, threeflavor QCD is known to be a completely Higgsed color superconductor that also spontaneously breaks $U(1)_B$. We argue that this highdensity phase is in fact a gapless SPT, with a gravitational thetaangle $\theta_g = \pi$ that safely coexists with the $U(1)_B$ NambuGoldstone boson. We explain why this SPT motivates unexpected transitions in the QCD phase diagram, as well as anomalous surface modes at the boundary of quarkmatter 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)