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Baryonic vortices in rotating nuclear matter

Kazuya Mameda, Muneto Nitta, Zebin Qiu

Abstract

We investigate baryonic vortices as topological excitations in rotating nuclear matter within the framework of chiral perturbation theory. We identify two distinct configurations: local and global vortices, both carrying the baryon number as the topological charge associated with the third homotopy group $π_3(S^3)$. For the local vortex, similar to the vortex Skyrmion in a finite isospin chemical potential, charged pions form the condensate on the boundary and have a phase winding, while the neutral pion varies along the rotation axis inside the vortex core. On the other hand, a global vortex is formed by the condensate and phase winding of the neutral pion, while the charged pions vary on the inside along the rotation axis. Crucially, although global vortices are usually discarded in infinite systems due to logarithmic divergence in energy, we demonstrate that the finite-size constraint dictated by causality in a rotating frame regularizes the divergence physically, rendering the global vortex a viable excitation. We reveal an energetic competition between global and local vortex states, under the tunable parameters of rotation, system size, and baryon chemical potential. Our results suggest that the previously overlooked global vortex can play a significant role in the topological structure of rotating dense QCD matter.

Baryonic vortices in rotating nuclear matter

Abstract

We investigate baryonic vortices as topological excitations in rotating nuclear matter within the framework of chiral perturbation theory. We identify two distinct configurations: local and global vortices, both carrying the baryon number as the topological charge associated with the third homotopy group . For the local vortex, similar to the vortex Skyrmion in a finite isospin chemical potential, charged pions form the condensate on the boundary and have a phase winding, while the neutral pion varies along the rotation axis inside the vortex core. On the other hand, a global vortex is formed by the condensate and phase winding of the neutral pion, while the charged pions vary on the inside along the rotation axis. Crucially, although global vortices are usually discarded in infinite systems due to logarithmic divergence in energy, we demonstrate that the finite-size constraint dictated by causality in a rotating frame regularizes the divergence physically, rendering the global vortex a viable excitation. We reveal an energetic competition between global and local vortex states, under the tunable parameters of rotation, system size, and baryon chemical potential. Our results suggest that the previously overlooked global vortex can play a significant role in the topological structure of rotating dense QCD matter.

Paper Structure

This paper contains 9 sections, 48 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Chiral Lagrangian under Rotation
  3. Local Vortices
  4. Global Vortices
  5. Numerical Results
  6. Parameter Ranges
  7. Zero Rotation
  8. Finite Rotation
  9. Conclusion and Outlook

Figures (3)

  • Figure 1: The string tension of local/global vortex solutions at zero rotation $\Omega=0$ and three typical values of the baryon chemical potential $\mu$, applied to QGP or neutron stars. For $R$ smaller than the presented ranges, $T(d)$ increases monotonically with an increasing $d$, yielding $d_0\rightarrow0$, which means there is no stable vortex solution with finite size.
  • Figure 2: The string tension of local/global vortex solutions as a function of $\Omega$ at different system radii $R$ and common baryon chemical potential $\mu=3.2f_\pi\simeq300\text{ MeV}$.
  • Figure 3: Critical angular velocity, energy density, and baryon density at $\mu=300\text{ MeV}$.