In the large flux limit vortices become flux tubes with almost constant magnetic field in the interior region. This occurs in the case of non-Abelian vortices as well, and the study of such configurations allows us to reveal a close relationship between vortex zero modes and the gyromagnetic instabilities of vector bosons in a strong background magnetic field discovered by Nielsen, Olesen and Ambjørn. The BPS vortices are exactly at the onset of this instability, and the dimension of their moduli space is precisely reproduced in this way. We present a unifying picture in which, through the study of the linear spectrum of scalars, fermions and W bosons in the magnetic field background, the expected number of translational, orientational, fermionic as well as semilocal zero modes is correctly reproduced in all cases.

The Ginzburg-Landau (GL) effective theory is a useful tool to study a superconductivity or superfluidity near the critical temperature, and usually the expansion up to the 4th order in terms of order parameters is sufficient for the description of the second-order phase transition. In this paper, we discuss the GL equation for the neutron 3 P2 superfluidity relevant for interior of neutron stars. We derive the GL expansion up to the 8th order in the condensates and find that this order is necessary for the system to have the unique ground state, unlike the ordinary cases. Starting from the LS potential, which provides the dominant attraction between two neutrons at the high density, we derive the GL equation in the path-integral formalism, where the auxiliary field method and the Nambu-Gor'kov representation are used. We present the detailed description for the trace calculation necessary in the derivation of the GL equation. As numerical results, we show the phase diagram of the neutron 3 P2 superfluidity on the plane spanned by the temperature and magnetic field, and find that the 8th order terms lead to a first-order phase transition, whose existence was predicted in the Bogoliubov-de Gennes equation but has not been found thus far within the framework of the GL expansion up to the 6th order. The first-order phase transition will affect the interior structures inside the neutron stars. I. INTRODUCTIONNeutron stars are one of the important astrophysical objects providing us laboratories of nuclear physics (see Refs. [1,2] for recent reviews). The extreme environments in the neutron stars, such as high density state, rapid rotation, strong magnetic field, strong gravitational field, and so on, lead to interesting questions about the unconventional states of nuclear systems. For example, it is considered that there can exist a various kind of matter phases inside the neutron stars: neutron rich gas and crusts at the surface, and neutron superfluidity, hyperon matter, π, K condensates, quark matter, etc., in the inside. Those states can be accessible from observations of the mass-radius relation, timeevolution of the surface temperature, neutrino emissions, and so on. The research of the equation of state is still an open question, and many efforts have been devoted to understand the massive neutron stars whose masses are almost twice as large as the solar mass [3,4]. One of the most recent observational developments were provided by the gravitational waves from the binary neutron star merger [5]. This finding opens a new era of researches of neutron *

Quark-hadron continuity was proposed as crossover between hadronic matter and quark matter without a phase transition, based on the matching of the symmetry and excitations in both phases. In the limit of a light strange-quark mass, it connects hyperon matter and the color-flavor-locked (CFL) phase exhibiting color superconductivity. Recently, it was proposed that this conjecture could be generalized in the presence of superfluid vortices penetrating both phases [1], and it was suggested that one hadronic superfluid vortex in hyperon matter could be connected to one non-Abelian vortex (color magnetic flux tube) in the CFL phase. Here, we argue that their proposal is consistent only at large distances; instead, we show that three hadronic superfluid vortices must combine with three non-Abelian vortices with different colors with the total color magnetic fluxes canceled out, where the junction is called a colorful boojum. We rigorously prove this in both a macroscopic theory based on the Ginzburg-Landau description in which symmetry and excitations match (including vortex cores), and a microscopic theory in which the Aharonov-Bohm phases of quarks around vortices match.

When a charged particle encircles around an Alice string, it changes the sign of the electric charge. In this paper we find a BPS-saturated Alice string in U(1)×SO(3) gauge theory with charged complex scalar fields belonging to the vector representation. After performing BPS completion we solve the BPS equations numerically. We further embed the Alice string into an N = 1 supersymmetric gauge theory to show that it is half BPS.