Abstract
We study QCD with massless quarks on ℝ3 × S1 under symmetry-twisted boundary conditions with small compactification radius, i.e. at high temperatures. Under suitable boundary conditions, the theory acquires a part of the center symmetry and it is spontaneously broken at high temperatures. We show that these vacua at high temperatures can be regarded as different symmetry-protected topological orders, and the domain walls between them support nontrivial massless gauge theories as a consequence of anomaly-inflow mechanism. At sufficiently high temperatures, we can perform the semi-classical analysis to obtain the domain-wall theory, and 2d U(Nc − 1) gauge theories with massless fermions match the ’t Hooft anomaly. We perform these analysis for the high-temperature domain wall of {mathbb{Z}}_{N_{mathrm{c}}} -QCD and also of Roberge-Weiss phase transitions.
Highlights
These interesting behaviors, confinement and chiral symmetry breaking, are the consequence of strong infrared dynamics, and it is usually very difficult to extract such information starting from QCD
We can find that the mixed anomaly between the gauge symmetry U(N − 1) and the discrete chiral symmetry (ZN )L cancels among N domain-wall fermions, and we find the following symmetry-protected topological (SPT) action for the ’t Hooft anomaly of the domain-wall theory, SSPT,DW
We find that the domain wall connecting distinct states related by the broken center symmetry supports U(N − 1) gauge theory with 2d massless Dirac fermions by explicit weak-coupling computation at sufficiently high temperatures
Summary
Roberge and Weiss showed that the QCD partition function has a fractional periodicity φ ∼ φ + 2π/Nc by the gauge invariance [55] That these is a Z2 center symmetry for quantized values of φ [31, 54], and we call it the RW parity At high temperatures, this RW parity is spontaneously broken, and there are two degenerate vacua with the mass gap as the three-dimensional quantum field theory. This RW parity is spontaneously broken, and there are two degenerate vacua with the mass gap as the three-dimensional quantum field theory We show that these distinct vacua can be regarded as the different SPT phases by studying the domain wall between them. The RW domain wall supports massless field theories by anomaly-inflow arguments
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