arXiv subjects
Publications and source records attributed to Muneto Nitta.
We clarify a relation between the Gross-Pitaevskii energy functional for spin-2 spinor Bose-Einstein condensates and the Ginzburg-Landau theory for neutron $^3P_2$ superfluidis (spin-triplet $P$-wave pairing with total angular momentum two). We then classify all uniform states with nontrivial unbroken symmetries, with the help of geometric invariant theory.
We find chiral non-Abelian vortices having windings only in one of the diquark condensations of left-handed and right-handed quarks in the color-flavor locked phase of dense QCD. They are the minimum vortices carrying half color magnetic fluxes of those of non-Abelian semi-superfluid vortices (color magnetic flux tubes) and 1/6 quantized superfluid circulations of Abelian superfluid vortices. These vortices carry ${\mathbb C}P^2$ orientational moduli in the internal space corresponding to their fluxes. The ${\mathbb C}P^2$ moduli of two chiral non-Abelian vortices with chiralities opposite to each other are energetically favored to be aligned while those of a vortex and anti-vortex to be orthogonal, and then these vortices attract each other. They are attached by chiral domain walls in the presence of the mass and axial anomaly terms explicitly breaking axial and chiral symmetries. We numerically show that two chiral non-Abelian vortices with chiralities opposite to each other are connected by a chiral domain wall, consisting a mesonic bound state which is nothing but a non-Abelian semi-superfluid vortex. We also show that Abelian and non-Abelian axial vortices attached by chiral domain walls are all unstable to decay into a set of chiral non-Abelian vortices. Furthermore, we find that chiral non-Abelian vortices exhibit unique features: one is the so-called topological obstruction implying that unbroken symmetry generators in the bulk are not defined globally around the vortices, and the other is color non-singlet Aharonov-Bohm (AB) phases implying that quarks encircling these vortices can detect the colors of magnetic fluxes of them at infinite distances.
${}^{3}P_{2}$ superfluids realized in neutron stars are the largest topological quantum matters in our Universe. We establish the existence and stability of non-Abelian half-quantum vortices (HQVs) in ${}^{3}P_{2}$ superfluids with strong magnetic fields. Using a self-consistent microscopic approach, we find that a singly quantized vortex is energetically destabilized into a pair of two non-Abelian HQVs owing to the strongly spin-orbit-coupled pairing. We find a topologically protected Majorana fermion on each HQV, thereby providing two-fold non-Abelian anyons characterized by both Majorana fermions and a non-Abelian first homotopy group.
We study higher-form global symmetries and a higher-group structure of a low-energy limit of $(3+1)$-dimensional axion electrodynamics in a gapped phase described by a topological action. We argue that the higher-form symmetries should have a semi-strict 4-group (3-crossed module) structure by consistency conditions of couplings of the topological action to background gauge fields for the higher-form symmetries. We find possible 't Hooft anomalies for the 4-group global symmetry, and discuss physical consequences.
The interior of a neutron star is expected to be occupied by a neutron $^3P_2$ superfluid, which is the condensate of spin-triplet $p$-wave Cooper pairs of neutrons with total angular momentum $J=2$. Here we investigate the thermodynamic stability of $^3P_2$ superfluids in a neutron-star interior under a strong magnetic field. Using the theory incorporating the finite size correction of neutron Fermi surface, we show that the spin-polarized phases of $^3P_2$ superfluids, the magnetized biaxial nematic phase and the ferromagnetic phase, appear in high temperatures and high magnetic fields. These phases were missed in the previous studies using the quasiclassical approximation in which dispersions of neutrons are linearized around the Fermi surface. In particular, the ferromagnetic phase, which is the condensation of Cooper-paired neutrons with fully polarized spins, appears between the normal phase and the biaxial nematic phase and enlarge the thermodynamic stability of $^3P_2$ superfluids under strong magnetic fields. Furthermore, we present the augmented Ginzburg-Landau theory that incorporates the thermodynamic stability of spin-polarized $^3P_2$ superfluid phases.
We construct a regular black hole solution on the orbifold ${\mathbb C}^{n}/{\mathbb Z}_{n}$ in the ($2n+1$)-dimensional Einstein-Maxwell theory. The event horizon is $S^{2n-1}/{\mathbb Z}_{n}$.
We find a novel confinement mechanism in the two-flavor dense quark matter proposed recently, that consists of the 2SC condensates and the $P$-wave diquark condensates of $d$-quarks. This quark matter exhibiting color superconductivity as well as superfluidity is classified into two phases; confined and deconfined phases of vortices. We establish that the criterion of the confinement is color neutrality of Aharonov-Bohm (AB) phases: vortices exhibiting color non-singlet AB phases are confined by the so-called AB defects to form color-singlet bound states. In the deconfined phase, the most stable vortices are non-Abelian Alice strings, which are superfluid vortices with fractional circulation and non-Abelian color magnetic fluxes therein, exhibiting color non-singlet AB phases. On the other hand, in the confined phase, these non-Abelian vortices are confined to either a baryonic or mesonic bound state in which constituent vortices are connected by AB defects. The baryonic bound state consists of three non-Abelian Alice strings with different color magnetic fluxes with the total flux canceled out connected by a domain wall junction, while the mesonic bound state consists of two non-Abelian Alice strings with the same color magnetic fluxes connected by a single domain wall. Interestingly, the latter contains a color magnetic flux in its core, but this can exist because of color neutrality of its AB phase.
We study the vacuum pair production by a time-dependent strong electric field based on the exact WKB analysis. We identify the generic structure of a Stokes graph for systems with the vacuum pair production and show that the number of produced pairs is given by a product of connection matrices for Stokes segments connecting pairs of turning points. We derive an explicit formula for the number of produced pairs, assuming the semi-classical limit. The obtained formula can be understood as a generalization of the divergent asymptotic series method by Berry, and is consistent with other semi-classical methods such as the worldline instanton method and the steepest descent evaluation of the Bogoliubov coefficients done by Brezin and Izykson. We also use the formula to discuss effects of time-dependence of the applied strong electric field including the interplay between the perturbative multi-photon pair production and non-peturbative Schwinger mechanism, and the dynamically assisted Schwinger mechanism.
We explore the effect of using two-dimensional matter-wave vortices to confine an ensemble of bosonic quantum impurities. This is modelled theoretically using a mass-imbalanced homogeneous two component Gross-Pitaevskii equation where each component has independent atom numbers and equal atomic masses. By changing the mass imbalance of our system we find the shape of the vortices are deformed even at modest imbalances, leading to barrel shaped vortices; which we quantify using a multi-component variational approach. The energy of impurity carrying vortex pairs are computed, revealing a mass-dependent energy splitting. We then compute the excited states of the impurity, which we in turn use to construct `covalent bonds' for vortex pairs. Our work opens a new route to simulating synthetic chemical reactions with superfluid systems.
Alice and Boojums are both representative characters created by Lewis Carroll. We show that they possibly meet in cores of rotating neutron stars. Recent studies of quark-hadron continuity suggest that neutron superfluid matter can connect smoothly to two-flavor symmetric quark matter at high densities. We study how this can be maintained in the presence of the vortices. In the neutron matter, quantized superfluid vortices arise. In the two-flavor dense quark matter, vortices carrying color magnetic fluxes together with fractionally quantized superfluid circulations appear as the most stable configuration, and we call these as the non-Abelian Alice strings. We show that three integer neutron superfluid vortices and three non-Abelian Alice strings of different color magnetic fluxes with total color flux canceled out are joined at a junction called a Boojum.
The recent discovery of an explicit solution of a black hole on the resolved orbifold ${\mathbb C}^n/{\mathbb Z}_n$ makes it possible to investigate the existence of $p$-branes on the orbifold. In particular, it is possible with reasonable precision to verify the prediction that an M2-brane on ${\mathbb C}^4/{\mathbb Z}_4$ in eleven dimensions and a D3-brane on ${\mathbb C}^3/{\mathbb Z}_3$ in ten dimensions have a family of black $p$-branes on the orbifold ${\mathbb C}^n/{\mathbb Z}_n$. These solutions are extremal and have regular horizons $S^{2n-1}/{\mathbb Z}_n$ without any naked singularity, with near horizon geometries AdS${}_{p+2}\times S^{2n-1}/{\mathbb Z}_n$.
We study two-body interactions of magnetic skyrmions on the plane and apply them to a (mostly) analytic description of a skyrmion lattice. This is done in the context of the solvable line, a particular choice of a potential for magnetic anisotropy and Zeeman terms, where analytic expressions for skyrmions are available. The energy of these analytic single skyrmion solutions is found to become negative below a critical point, where the ferromagnetic state is no longer the lowest energy state. This critical value is determined exactly without the ambiguities of numerical simulations. Along the solvable line the interaction energy for a pair of skyrmions is repulsive with power law fall off in contrast to the exponential decay of a purely Zeeman potential term. Using the interaction energy expressions we construct an inhomogeneous skyrmion lattice state, which is a candidate ground states for the model in particular parameter regions. Finally we estimate the transition between the skyrmion lattice and an inhomogeneous spiral state.
Quark-hadron continuity with two-flavor quarks that was proposed recently connects hadronic matter with neutron $^3P_2$ superfluidity and two-flavor dense quark matter. This two-flavor dense quark phase consists of the coexistence of the 2SC condensates and the $P$-wave diquark condensates of $d$-quarks, which gives rise to color superconductivity as well as superfluidity. We classify vortices in this phase. The most stable vortices are what we call the non-Abelian Alice strings, which are superfluid vortices with non-Abelian color magnetic fluxes therein, exhibiting so-called topological obstruction, or a non-Abelian generalization of the Alice property. We show that a single Abelian superfluid vortex is unstable against decay into three non-Abelian Alice strings. We discover that a non-Abelian Alice string carries orientational moduli of the real projective space $\mathbb{R}P^2$ corresponding to the color flux therein in the presence of the $P$-wave condensates alone. We calculate Aharanov-Bohm (AB) phases around the non-Abelian Alice string, and find that the 2SC condensates and string's orientational moduli must be aligned with each other because of single-valuedness of the AB phases of the 2SC condensates.
Strings in $\mathcal{N}=2$ supersymmetric ${\rm U}(1)^N$ gauge theories with $N$ hypermultiplets are studied in the generic setting of an arbitrary Fayet-Iliopoulos triplet of parameters for each gauge group and an invertible charge matrix. Although the string tension is generically of a square-root form, it turns out that all existing BPS (Bogomol'nyi-Prasad-Sommerfield) solutions have a tension which is linear in the magnetic fluxes, which in turn are linearly related to the winding numbers. The main result is a series of theorems establishing three different kinds of solutions of the so-called constraint equations, which can be pictured as orthogonal directions to the magnetic flux in ${\rm SU}(2)_R$ space. We further prove for all cases, that a seemingly vanishing Bogomol'nyi bound cannot have solutions. Finally, we write down the most general vortex equations in both master form and Taubes-like form. Remarkably, the final vortex equations essentially look Abelian in the sense that there is no trace of the ${\rm SU}(2)_R$ symmetry in the equations, after the constraint equations have been solved.
We investigate a higher-group structure of massless axion electrodynamics in $(3+1)$ dimensions. By using the background gauging method, we show that the higher-form symmetries necessarily have a global semistrict 3-group (2-crossed module) structure, and exhibit 't Hooft anomalies of the 3-group. In particular, we find a cubic mixed 't Hooft anomaly between 0-form and 1-form symmetries, which is specific to the higher-group structure.
We formulate four-dimensional $\mathcal{N} = 1$ supersymmetric nonlinear sigma models on Hermitian symmetric spaces with higher derivative terms, free from the auxiliary field problem and the Ostrogradski's ghosts, as gauged linear sigma models. We then study Bogomol'nyi-Prasad-Sommerfield equations preserving 1/2 or 1/4 supersymmetries. We find that there are distinct branches, that we call canonical ($F=0$) and non-canonical ($F\neq 0$) branches, associated with solutions to auxiliary fields $F$ in chiral multiplets. For the ${\mathbb C}P^N$ model, we obtain a supersymmetric ${\mathbb C}P^N$ Skyrme-Faddeev model in the canonical branch while in the non-canonical branch the Lagrangian consists of solely the ${\mathbb C}P^N$ Skyrme-Faddeev term without a canonical kinetic term. These structures can be extended to the Grassmann manifold $G_{M,N} = SU(M)/[SU(M-N)\times SU(N) \times U(1)]$. For other Hermitian symmetric spaces such as the quadric surface $Q^{N-2}=SO(N)/[SO(N-2) \times U(1)])$, we impose F-term (holomorphic) constraints for embedding them into ${\mathbb C}P^{N-1}$ or Grassmann manifold. We find that these constraints are consistent in the canonical branch but yield additional constraints on the dynamical fields thus reducing the target spaces in the non-canonical branch.
We investigate effects of thermal and quantum fluctuations of the superfluid order parameter in $^1S_{0}$ superfluids in neutron stars. We construct a separable potential to reproduce the $^1S_{0}$ phase shift reconstructed by using the partial wave analysis from nucleon scattering data. We include superfluid fluctuations within a strong-coupling approximation developed by Nozières and Schmitt-Rink and determine self-consistently the superfluid order parameter as well as the chemical potential. We show that the quantum depletion, which gives a fraction of noncondensed neutrons at zero temperature due to quantum pairing fluctuations, plays an important role not only near the critical temperature from superfluid states to normal states but also at zero temperature. We derive the dispersion relation of Anderson-Bogoliubov modes associated with phase fluctuations, and show also that there is a nonzero fraction of noncondensed components in the neutron number as a result of the strong-coupling effect. Our results indicate that superfluid fluctuations are important for thermodynamic properties in neutron stars.
We argue that strings (vortices) and monopoles are confined, when fields receiving nontrivial Aharonov-Bohm (AB) phases around a string develop vacuum expectation values (VEVs). We illustrate this in an $SU(2) \times U(1)$ gauge theory with charged triplet complex scalar fields admitting Alice strings and monopoles, by introducing charged doublet scalar fields receiving nontrivial AB phases around the Alice string. The Alice string carries a half $U(1)$ magnetic flux and $1/4$ $SU(2)$ magnetic flux taking a value in two of the $SU(2)$ generators characterizing the $U(1)$ modulus. This string is not confined in the absence of a doublet VEV in the sense that the $SU(2)$ magnetic flux can be detected at large distance by an AB phase around the string. When the doublet field develops VEVs, there appear two kinds of phases that we call deconfined and confined phases. When a single Alice string is present in the deconfined phase, the $U(1)$ modulus of the string and the vacuum moduli are locked (the bulk-soliton moduli locking). In the confined phase, the Alice string is inevitably attached by a domain wall that we call an AB defect and is confined with an anti-Alice string or another Alice string with the same $SU(2)$ flux. Depending on the partner, the pair annihilates or forms a stable doubly-wound Alice string having an $SU(2)$ magnetic flux inside the core, whose color cannot be detected at large distance by AB phases, implying the "color" confinement. The theory also admits stable Abrikosov-Nielsen-Olesen string and a ${\mathbb Z}_2$ string in the absence of the doublet VEVs, and each decays into two Alice strings in the presence of the doublet VEVs. A monopole in this theory can be constructed as a closed Alice string with the $U(1)$ modulus twisted once, and we show that with the doublet VEVs, monopoles are also confined to monopole mesons of the monopole charge two.