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Imaginary Rotation Breaks Charge Conjugation in Hot QCD

  • Rin Takada
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Abstract

Starting from the identity e2πi Jz=(−1)F=eiπQ on the color-singlet physical state space, we derive a density-operator identity that ties imaginary rotation to an imaginary quark chemical potential, ρ(ΩI+2π,θq)=ρ(ΩI,θq+π). Hence imaginarily rotating SU(3) QCD at (ΩI,θq)=(2π,0) is mapped exactly onto the Roberge-Weiss (RW) point (0,π), where charge conjugation C is spontaneously broken above the RW endpoint---a conclusion independent of any model or approximation. Minimizing the one-loop effective potential on the rotation axis, we obtain analytically, for three massless flavors, the second-order transition at ΩI,C/π=(22−2√(22))/9, and a subsequent first-order transition at ΩI,lock/π=2/3+2√(111)/27. At smaller ΩI, a continuous degeneracy of the massless one-loop approximation leaves the realization of C undecided; a finite strange-quark mass lifts it. We also state how the exact relations and the on-axis predictions can be tested in lattice QCD.

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Cite

BibTeXRIS
BibTeX
@misc{takada2026imaginary,
  title = {{Imaginary Rotation Breaks Charge Conjugation in Hot QCD}},
  author = {Rin Takada},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.25849},
  eprint = {2608.25849},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.25849},
}
RIS
TY  - UNPB
TI  - Imaginary Rotation Breaks Charge Conjugation in Hot QCD
AU  - Rin Takada
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.25849
UR  - https://arxiv.org/abs/2608.25849
AB  - Starting from the identity e^2πi J_z=(−1)^F=e^iπQ on the color-singlet physical state space, we derive a density-operator identity that ties imaginary rotation to an imaginary quark chemical potential, ρ(Ω_I+2π,θ_q)=ρ(Ω_I,θ_q+π). Hence imaginarily rotating SU(3) QCD at (Ω_I,θ_q)=(2π,0) is mapped exactly onto the Roberge-Weiss (RW) point (0,π), where charge conjugation C is spontaneously broken above the RW endpoint---a conclusion independent of any model or approximation. Minimizing the one-loop effective potential on the rotation axis, we obtain analytically, for three massless flavors, the second-order transition at Ω_I,C/π=(22−2√(22))/9, and a subsequent first-order transition at Ω_I,lock/π=2/3+2√(111)/27. At smaller Ω_I, a continuous degeneracy of the massless one-loop approximation leaves the realization of C undecided; a finite strange-quark mass lifts it. We also state how the exact relations and the on-axis predictions can be tested in lattice QCD.
ER  -