We review our recent work on solitons in the Higgs phase. use U(NC) gauge theory with NF scalar fields fundamental representation, which can be extended to possess eight supercharges. propose moduli matrix as a tool exhaust all BPS solutions, and characterize possible parameters. Moduli spaces of domain walls (kinks) vortices, are only elementary phase, found terms matrix. Stable monopoles instantons exist phase if they attached by vortices form composite solitons. The these also worked out...

We completely determine the moduli space ${\mathcal{M}}_{N,k}$ of $k$ vortices in $U(N)$ gauge theory with $N$ Higgs fields fundamental representation. Its open subset for separated is found as symmetric product $(\mathbf{C}\ifmmode\times\else\texttimes\fi{}\mathbf{C}{P}^{N\ensuremath{-}1}{)}^{k}/{\mathfrak{S}}_{k}$. Orbifold singularities this correspond to coincident and are resolved resulting a smooth manifold. The relation K\"ahler quotient construction discussed.

We study a $1/4$ Bogomol'nyi-Prasad-Sommerfield equation containing configurations made of walls, vortices, and monopoles in the Higgs phase, using supersymmetric $U({N}_{\mathrm{C}})$ gauge theories with eight supercharges ${N}_{\mathrm{F}}$ fundamental hypermultiplets. find total moduli space to be quotient holomorphic maps from complex plane ${N}_{\mathrm{C}}\ifmmode\times\else\texttimes\fi{}{N}_{\mathrm{F}}$ matrix divided by $GL({N}_{\mathrm{C}},\mathbf{C})$. obtain all possible...

We demonstrate that the three-dimensional Skyrmion, which has remained elusive so far, spontaneously appears as ground state of SU(2) symmetric Bose-Einstein condensates coupled with a non-Abelian gauge field. The field is analogue Rashba spin-orbit coupling. Upon squashing SO(3) to one- or two-dimensional shapes, we find continuously undergoes change from identified by estimating winding numbers and helicity. All emerged Skyrmions are physically understandable concept helical modulation in...

Abstract Dense quantum chromodynamic matter accommodates various kind of topological solitons such as vortices, domain walls, monopoles, kinks, boojums, and so on. In this review, we discuss properties in dense chromodynamics (QCD) their phenomenological implications. Particular emphasis is placed on the color–flavor-locked (CFL) phase, which exhibits both superfluidity superconductivity. The are discussed terms effective field theories Ginzburg–Landau theory, chiral Lagrangian, or...

We show that knots of spin textures can be created in the polar phase a spin-1 Bose-Einstein condensate, and discuss experimental schemes for their generation probe, together with lifetime.

We investigate a higher-group structure of massless axion electrodynamics in $(3+1)$ dimensions. By using the background gauging method, we show that higher-form symmetries necessarily have global semistrict 3-group (2-crossed module) structure, and exhibit 't Hooft anomalies 3-group. In particular, find cubic mixed anomaly between 0-form 1-form symmetries, which is specific to structure.

We study higher-form symmetries in a low-energy effective theory of massless axion coupled with photon $(3+1)$ dimensions. It is shown that the this system are accompanied by semistrict 3-group (2-crossed module) structure, which can be found correlation functions symmetry generators symmetries. argue Witten effect and anomalous Hall electrodynamics described terms transformations.

A bstract Based on the chiral perturbation theory at leading order, we show a signal of presence new phase in rapidly rotating QCD matter with two flavors, that is domain-wall Skyrmion phase. Lagrangian Wess-Zumino-Witten (WZW) term responsible for anomaly and vortical effect, it was shown ground state soliton lattice (CSL) consisting stack η -solitons high density region under rapid rotation. In large parameter region, single -soliton decays into pair non-Abelian solitons, each which...

When instantons are put into the Higgs phase, vortices attached to instantons. We construct such composite solitons as $1/4$ BPS states in five-dimensional supersymmetric $U({N}_{\mathrm{C}})$ gauge theory with ${N}_{\mathrm{F}}(\ensuremath{\ge}{N}_{\mathrm{C}})$ fundamental hypermultiplets. solve hypermultiplet equation and show that all solutions generated by an ${N}_{\mathrm{C}}\ifmmode\times\else\texttimes\fi{}{N}_{\mathrm{F}}$ matrix which is holomorphic two complex variables, assuming...

We make a detailed study of the moduli space winding number two (k=2) axially symmetric vortices (or equivalently, co-axial composite fundamental vortices), occurring in U(2) gauge theory with flavors Higgs phase, recently discussed by Hashimoto-Tong (hep-th/0506022) and Auzzi-Shifman-Yung (hep-th/0511150). find that it is weighted projective WCP^2_(2,1,1)=CP^2/Z_2. This manifold contains an A_1-type (Z_2) orbifold singularity even though full including relative position smooth. The SU(2)...

We present a systematic method to construct exactly all Bogomol'nyi-Prasad-Sommerfield multiwall solutions in supersymmetric $\mathrm{U}({N}_{\mathrm{C}})$ gauge theories five dimensions with ${N}_{\mathrm{F}}$ hypermultiplets the fundamental representation for infinite coupling. The moduli space of these non-Abelian walls is found be complex Grassmann manifold...

The Bogomol'nyi-Prasad-Sommerfield (BPS) multiwall solutions are constructed in supersymmetric $\mathrm{U}({N}_{\mathrm{C}})$ gauge theories five dimensions with ${N}_{\mathrm{F}}(>{N}_{\mathrm{C}})$ hypermultiplets the fundamental representation. Exact obtained full generic moduli for infinite coupling and partial finite coupling. wall require nontrivial configurations either fields or off diagonal components of adjoint scalars depending on gauge. Effective as world volume theories....

We study Bogomol'nyi-Prasad-Sommerfield (BPS) non-Abelian semilocal vortices in $U({N}_{\mathrm{C}})$ gauge theory with ${N}_{\mathrm{F}}$ flavors, ${N}_{\mathrm{F}}>{N}_{\mathrm{C}}$, the Higgs phase. The moduli space for an arbitrary winding number is described using matrix formalism. find a relation between spaces of Seiberg-like dual pairs theories, and $U({N}_{\mathrm{F}}\ensuremath{-}{N}_{\mathrm{C}})$. They are two alternative regularizations parent non-Hausdorff space, which tend to...

The most fundamental strings in high-density color superconductivity are the non-Abelian semisuperfluid which have color-gauge flux tubes but behave as superfluid vortices energetic point of view. We show that addition to usual translational zero modes, these normalizable orientational modes internal space, associated with color-flavor locking symmetry broken presence strings. interaction among two parallel is derived for general relative universal repulsion. This implies previously known...

We study the asymptotic interaction between two half-quantized vortices in two-component Bose-Einstein condensates. When different components are placed at distance $2R$, leading order of force them is found to be $(\mathrm{ln}R/\ensuremath{\xi}\ensuremath{-}1/2)/{R}^{3}$, contrast $1/R$ same component. derive it analytically using Abrikosov ansatz and profile functions vortices, confirmed numerically with Gross-Pitaevskii model. also find that short-range cutoff intervortex potential...

We show that local and semilocal strings in Abelian non-Abelian gauge theories with critical couplings always reconnect classically collision, by using moduli space approximation. The matrix formalism explicitly identifies a well-defined set of the vortex parameters. Our analysis generic geodesic motion terms those shows right-angle scattering head-on collision two vortices, which is known to give reconnection strings.

We investigate the collision dynamics of two non-Abelian vortices and find that, unlike Abelian vortices, they neither reconnect themselves nor pass through each other, but create a rung between them in topologically stable manner. Our predictions are verified using model cyclic phase spin-2 spinor Bose-Einstein condensate.

We construct a low-energy effective theory describing non-Abelian vortices in the color superconducting quark matter under stress. demonstrate that all are radically unstable against decay into only one type of due to potential term induced by explicit flavor symmetry breaking strange mass. A simple analytical estimate for lifetime is provided controlled weak-coupling calculations. briefly discuss (non)existence magnetic monopoles at high density.

We study the effects of internal coherent (Rabi) coupling in vortex lattices two-component BECs under rotation. find how without Rabi known before are connected to Abrikosov lattice integer vortices with increasing coupling. that (1) for small couplings, fractional a triangular or square large intercomponent constitute hexamers tetramers, namely multidimer bound states made six four vortices, respectively, (2) these broken into set dimers at intermediate and (3) change their partners various...

We study classical configurations in the $$ \mathbb{C} P N −1 model on \mathbb{R} 1 × S with twisted boundary conditions. focus specific composed of multiple fractionalized-instantons, termed "neutral bions", which are identified as "perturbative infrared renormalons" by Ünsal and his collaborators. For \mathbb{Z} conditions, we consider an explicit ansatz corresponding to topologically trivial containing one fractionalized instanton (ν = 1/N ) anti-instanton −1/N at large separations,...

We study higher-form symmetries and a higher group in the low energy limit of $(3+1)$-dimensional axion electrodynamics with massive photon. A topological field theory describing excitations axion-photon coupling, which we call electrodynamics, is obtained limit. Higher-form are specified by equations motion Bianchi identities. find that there induced anyons on intersections symmetry generators. By link worldlines anyons, show worldvolume an axionic domain wall topologically ordered. further...

A bstract We study the vacuum pair production by a time-dependent strong electric field based on exact WKB analysis. identify generic structure of Stokes graph for systems with and show that number produced pairs is given product connection matrices segments connecting turning points. derive an explicit formula pairs, assuming semi-classical limit. The obtained can be understood as generalization divergent asymptotic series method Berry, consistent other methods such worldline instanton...

Domain-wall skyrmions are trapped inside a domain wall. We investigate domain-wall in chiral magnets using fully analytic approach. Treating the Dzyaloshinskii-Moriya (DM) interaction perturbatively, we construct low-energy effective theory of magnetic wall an $O(3)$ sigma model with DM and easy-axis potential term, yielding sine-Gordon model. then as solitons along also on top pair anti-domain One characteristic feature is that both antiskyrmions equally stable wall, unlike bulk which only...

A bstract The ground state of QCD with two flavors at a finite baryon chemical potential under rapid rotation is chiral soliton lattice (CSL) the η meson, consisting stack sine-Gordon solitons carrying number, due to anomalous coupling meson rotation. In large parameter region, becomes non-Abelian CSL, in which neutral pion condensation each decays into pair S 2 moduli originated from Nambu-Goldstone (NG) modes localized around it, corresponding spontaneously broken vector symmetry SU(2) V ....