Global 4-group symmetry and t Hooft anomalies in topological axion electrodynamics

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.

Topological axion electrodynamics and 4-group symmetry

We study higher-form symmetries and a higher group in $(3+1)$-dimensional axion electrodynamics where the axion and photon are massive. A topological field theory describing topological excitations with the axion-photon coupling is obtained in the low energy limit, in which higher-form symmetries are specified. By using intersections of the symmetry generators, we find that the worldvolume of an axionic domain wall is topologically ordered. We further specify the underlying mathematical structure elegantly describing all salient features of the theory to be a 4-group.

Non-Abelian Half-Quantum Vortices in ${}^{3}P_{2}$ Topological Superfluids

The existence and stability of non-Abelian half-quantum vortices (HQVs) are established in ${}^{3}P_{2}$ superfluids in neutron stars with strong magnetic fields, the largest topological quantum matter in our Universe. Using a self-consistent microscopic framework, we find that one integer vortex is energetically destabilized into a pair of two non-Abelian HQVs due to the strong spin-orbit coupled gap functions. 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.

Dispersive 1D Majorana modes with emergent supersymmetry in 1D proximitized superconductors via spatially-modulated potentials and magnetic fields

In condensed matter systems, zero-dimensional or one-dimensional Majorana modes can be realized respectively as the end and edge states of one-dimensional and two-dimensional topological superconductors. In this $textit{top-down}$ approach, $(d-1)$-dimensional Majorana modes are obtained as the boundary states of a topologically nontrivial $d$-dimensional bulk. In a $textit{bottom-up}$ approach instead, $d$-dimensional Majorana modes in a $d$-dimensional system can be realized as the continuous limit of a periodic lattice of coupled $(d-1)$-dimensional Majorana modes. We illustrate this idea by considering one-dimensional proximitized superconductors with spatially-modulated potential or magnetic fields. The ensuing inhomogenous topological state exhibits one-dimensional counterpropagating Majorana modes with finite dispersion, and with a Majorana gap which can be controlled by external fields. In the massless case, the Majorana modes have opposite Majorana polarizations and pseudospins, are conformally invariant, and realize centrally extended quantum mechanical supersymmetry. The supersymmetry exhibits spontaneous partial breaking. Consequently, the massless Majorana fermion can be identified as a Goldstino, i.e., the Nambu-Goldstone fermion associated with the spontaneously broken supersymmetry.

1D Majorana Goldstinos and extended supersymmetry in quantum wires

One-dimensional Majorana modes can be obtained as boundary excitations of topologically nontrivial two-dimensional topological superconductors. Here, we propose instead the bottom-up creation of one-dimensional, counterpropagating, and dispersive Majorana modes as bulk excitations of a periodic chain of partially-overlapping, zero-dimensional Majorana modes in proximitized quantum nanowires via periodically-modulated magnetic fields. These dispersive one-dimensional Majorana modes can be either massive or massless. Massless Majorana modes are pseudohelical, having opposite Majorana pseudospin, and realize emergent quantum mechanical supersymmetry. The system exhibits extended supersymmetry with central extensions and with spontaneous partial breaking. We identify the massless Majorana fermions as Goldstinos, i.e., the Nambu-Goldstone fermions associated with the spontaneous breaking of supersymmetry. The experimental fingerprint of massless Majorana modes and supersymmetry is the presence of a finite zero-bias peak, which is generally not expected for Majorana modes with a finite overlap and localized at a finite distance. Moreover, slowly varying magnetic fields can realize an adiabatic Majorana pump which can be used as a dynamically probe of topological superconductivity.

Topological confinement of vortices in two-flavor dense QCD

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.

Minimum non-Abelian vortices and their confinement in three flavor dense QCD

We find chiral non-Abelian semi-superfluid vortices in the color-flavor locked (CFL) phase of dense QCD as 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 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. They are confined by chiral domain walls in the presence of the mass and axial anomaly terms explicitly breaking axial and chiral symmetries while they are deconfined in the absence of those terms. In the confined phase, two chiral non-Abelian semi-superfluid vortices with chiralities opposite to each other are connected by a chiral domain wall, consisting a mesonic bound state exhibiting only color singlet AB phases so that the quarks cannot detect the color of magnetic flux of such a bound state at infinite distances, and the final state of the mesonic bound state 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.

Exact Phase Structure of One Dimensional Chiral Magnets

We determine exactly the phase structure of a chiral magnet in one spatial dimension with the Dzyaloshinskii-Moriya (DM) interaction and a potential that is a function of the third component of the magnetization vector, $n_3$, with a Zeeman (linear with the coefficient $B$) term and an anisotropy (quadratic with the coefficient $A$) term. For large values of potential parameters $A$ and $B$, the system is in one of the ferromagnetic phases, whereas it is in the spiral phase for small values. In the spiral phase we find a continuum of spiral solutions, which are one-dimensionally modulated solutions with various periods. The ground state is determined as the spiral solution with the lowest average energy density. As the phase boundary approaches, the period of the lowest energy spiral solution diverges, and the spiral solutions become domain wall solutions with zero energy at the boundary. The energy of then domain wall solutions is positive in the homogeneous phase region, but is negative in the spiral phase region, signaling the instability of the homogeneous (ferromagnetic) state. The order of the phase transition between spiral and homogeneous phases and between polarized ($n_3=pm 1$) and canted ($n_3 ot=pm 1$) ferromagnetic phases is found to be second order.

Higher Derivative Supersymmetric Nonlinear Sigma Models on Hermitian Symmetric Spaces, and BPS States Therein

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 Ostrogradskis ghosts, as gauged linear sigma models. We then study Bogomolnyi-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 ($F eq 0$) 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.

Synthetic superfluid chemistry with vortex-trapped quantum impurities

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.