Inhibition of the splitting of the chiral and deconfinement transition due to rotation in QCD: The phase diagram of the linear sigma model coupled to Polyakov loops

We discuss the effect of rigid rotation on the critical temperatures of deconfinement and chiral transitions in the linear sigma model coupled to quarks and the Polyakov loop. We point out the essential role of the causality condition, which requires that any point of the system should rotate slower than the velocity of light. We show that imposing this physical requirement leads to inhibition of the splitting between the chiral and confining transitions, which becomes negligibly small (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Δ</a:mi><a:mi>T</a:mi><a:mo>∼</a:mo><a:mn>1</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>MeV</a:mi></a:math> or less) for experimentally relevant, slow angular velocities <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi mathvariant="normal">Ω</d:mi><d:mo>∼</d:mo><d:mn>10</d:mn><d:mtext> </d:mtext><d:mtext> </d:mtext><d:mi>MeV</d:mi></d:math> of a (5–10) fm-sized systems. Moreover, the boundedness of the system has a much bigger effect on temperature splitting than the rotation itself: the splitting reaches 10 MeV in a small, one-fermi-sized nonrotating system. The temperature splitting may, however, become enhanced in an academic limit of ultrarelativistic regimes when the boundary of the system rotates at near-to-light velocities. Published by the American Physical Society 2024