Spontaneous chiral-symmetry breaking in four-dimensional QCD with Ax=Ay=0 projection in dimensional reduction gauge
Abstract
We investigate spontaneous chiral-symmetry breaking in four-dimensional (4D) QCD in the dimensional reduction (DR) gauge, defined so as to minimize RDR≡ ∫ d4s Tr [ Ax2(s) + Ay2(s) ]. We consider ``tz-projection" of Ax,y(s) → 0 and ``xy-projection" of At,z(s) → 0, respectively, for the gauge configuration generated in the DR gauge, in a similar sense to Abelian, monopole and photon projections in the maximally Abelian gauge. The chiral condensate is estimated from the low-lying Dirac-eigenvalue density ρ(λ) using the Banks-Casher relation. By the tz-projection in the DR gauge, the chiral condensate is largely reserved. In contrast, the chiral condensate becomes zero by the xy-projection in the DR gauge. This indicates that At(s) and Az(s) play a dominant role, while Ax(s) and Ay(s) play no role, in spontaneous chiral-symmetry breaking in the DR gauge.
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BibTeX
@misc{tohme2026spontaneous,
title = {{Spontaneous chiral-symmetry breaking in four-dimensional QCD with $A_x=A_y=0$ projection in dimensional reduction gauge}},
author = {Kei Tohme and Hideo Suganuma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30850},
eprint = {2610.30850},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30850},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spontaneous chiral-symmetry breaking in four-dimensional QCD with A_x=A_y=0 projection in dimensional reduction gauge
AU - Kei Tohme
AU - Hideo Suganuma
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30850
UR - https://arxiv.org/abs/2610.30850
AB - We investigate spontaneous chiral-symmetry breaking in four-dimensional (4D) QCD in the dimensional reduction (DR) gauge, defined so as to minimize R_DR≡ ∫ d^4s Tr [ A_x^2(s) + A_y^2(s) ]. We consider ``tz-projection" of A_x,y(s) → 0 and ``xy-projection" of A_t,z(s) → 0, respectively, for the gauge configuration generated in the DR gauge, in a similar sense to Abelian, monopole and photon projections in the maximally Abelian gauge. The chiral condensate is estimated from the low-lying Dirac-eigenvalue density ρ(λ) using the Banks-Casher relation. By the tz-projection in the DR gauge, the chiral condensate is largely reserved. In contrast, the chiral condensate becomes zero by the xy-projection in the DR gauge. This indicates that A_t(s) and A_z(s) play a dominant role, while A_x(s) and A_y(s) play no role, in spontaneous chiral-symmetry breaking in the DR gauge.
ER -