Domain-wall Skyrmion phase in a rapidly rotating QCD matter

Abstract

Based on the chiral perturbation theory at the leading order, we show the presence of a new phase in rapidly rotating QCD matter with two flavors, that is a domain-wall Skyrmion phase. Based on the chiral Lagrangian with a Wess-Zumino-Witten (WZW) term responsible for the chiral anomaly and chiral vortical effect, it was shown that the ground state is a chiral soliton lattice(CSL) consisting of a stack of $\hat{I}\cdot$-solitons in a high density region under rapid rotation. In a large parameter region, a single $\hat{I}\cdot$-soliton decays into a pair of non-Abelian solitons, each of which carries $\mathrm{SU}(2{)}_{\mathrm{V}}/\mathrm{U}(1)\simeq \mathbb{C}{P}^1\simeq S^2$ moduli as a consequence of the spontaneously broken vector symmetry $\mathrm{SU}(2{)}_{\mathrm{V}}$. In such a non-Abelian CSL, we construct the effective world-volume theory of a single non-Abelian soliton to obtain a $d=2+1$ dimensional $\mathbb{C}{P}^1$ model with a topological term originated from the WZW term. We show that when the chemical potential is larger than a critical value, a topological lump supported by the second homotopy group $\ddot{I}{€}_2(S^2)\simeq \mathbb{Z}$ has negative energy and is spontaneously created, implying the domain-wall Skyrmion phase. This lump corresponds in the bulk to a Skyrmion supported by the third homotopy group $\ddot{I}{€}_3[\mathrm{SU}(2)]\simeq \mathbb{Z}$ carrying a baryon number. This composite state is called a domain-wall Skyrmion, and is stable even in the absence of the Skyrme term. An analytic formula for the effective nucleon mass in this medium is obtained as $4\sqrt{2}\ddot{I}€f_{\ddot{I}}€f_{\hat{I}}\cdot /m_{\ddot{I}}€\sim 1.21$ GeV with the decay constants $f_{\ddot{I}}€$ and $f_{\hat{I}}\cdot$ of the pions and $\hat{I}\cdot$ meson, respectively, and the pion mass $m_{\ddot{I}}€$, which is surprisingly close to the nucleon mass in the QCD vacuum.

20 pages, 3 figures, v2: references added