Spin-One Secondary Pairing in Two-Flavor Color Superconductivity: Spinful Relativistic Superfluidity and Anomaly Matching
Abstract
We study secondary pairing in the two-flavor color-superconducting (2SC) phase, where the residual ungapped quarks form a same-chirality JP=1+ condensate driven by an attractive instanton-induced interaction. We determine its symmetry realization, quasiparticle structure, anomaly matching, and low-energy effective theory. The pairing gap is necessarily nodal; in particular, the complex axial state has two point nodes and realizes a spinful relativistic superfluid. This state preserves the full chiral symmetry SU(2)L×SU(2)R while breaking the modified baryon-number symmetry U(1)B̃ and spatial rotations, with rotations about the nodal axis locked to the condensate phase. This locking gives rise to a Berry term, the Mermin-Ho relation, and a type-B orientational Nambu-Goldstone mode in addition to the superfluid phonon. We also show how anomaly matching is reorganized by secondary pairing: the perturbative mixed SU(2)L,R2U(1)B̃ anomaly is realized by a Wess-Zumino coupling of the superfluid phonon, whereas the SU(2)L and SU(2)R Witten anomalies are carried by the point-node Bogoliubov-de Gennes flavor doublets. The resulting theory provides a concrete dense-QCD realization of a spinful relativistic superfluid with nodal fermions required by anomaly matching.
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BibTeX
@misc{yamamoto2026spinone,
title = {{Spin-One Secondary Pairing in Two-Flavor Color Superconductivity: Spinful Relativistic Superfluidity and Anomaly Matching}},
author = {Naoki Yamamoto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24472},
eprint = {2609.24472},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24472},
}
RIS
TY - UNPB
TI - Spin-One Secondary Pairing in Two-Flavor Color Superconductivity: Spinful Relativistic Superfluidity and Anomaly Matching
AU - Naoki Yamamoto
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24472
UR - https://arxiv.org/abs/2609.24472
AB - We study secondary pairing in the two-flavor color-superconducting (2SC) phase, where the residual ungapped quarks form a same-chirality J^P=1^+ condensate driven by an attractive instanton-induced interaction. We determine its symmetry realization, quasiparticle structure, anomaly matching, and low-energy effective theory. The pairing gap is necessarily nodal; in particular, the complex axial state has two point nodes and realizes a spinful relativistic superfluid. This state preserves the full chiral symmetry SU(2)_L×SU(2)_R while breaking the modified baryon-number symmetry U(1)_B̃ and spatial rotations, with rotations about the nodal axis locked to the condensate phase. This locking gives rise to a Berry term, the Mermin-Ho relation, and a type-B orientational Nambu-Goldstone mode in addition to the superfluid phonon. We also show how anomaly matching is reorganized by secondary pairing: the perturbative mixed SU(2)_L,R^2U(1)_B̃ anomaly is realized by a Wess-Zumino coupling of the superfluid phonon, whereas the SU(2)_L and SU(2)_R Witten anomalies are carried by the point-node Bogoliubov-de Gennes flavor doublets. The resulting theory provides a concrete dense-QCD realization of a spinful relativistic superfluid with nodal fermions required by anomaly matching.
ER -