Single Meron Research Articles

Topological Objects in Holographic QCD

We study topological objects in holographic QCD based on the Sakai-Sugimoto model, which is constructed with Nc D4 branes and Nf D8/ branes in the superstring theory, and is infrared equivalent to 1 + 3 dimensional massless QCD. Using the gauge/gravity duality, holographic QCD is described as 1 + 4 dimensional U(Nf) gauge theory in flavor space with a background gravity, and its instanton solutions correspond to baryons. First, using the Witten Ansatz, we reduce holographic QCD into a 1 + 2 dimensional Abelian Higgs theory in a curved space and consider its topological aspect. We numerically obtain the Abrikosov vortex solution and investigate single baryon properties. Second, we study a single meron and two merons in holographic QCD. The single meron carrying a half-integer baryon number is found to have an infinite energy also in holographic QCD. We propose a new-type baryon excitation of the two-merons oscillation in the extra-direction of holographic QCD.

Creation and annihilation of topological meron pairs in in-plane magnetized films

Merons which are topologically equivalent to one-half of skyrmions can exist only in pairs or groups in two-dimensional (2D) ferromagnetic (FM) systems. The recent discovery of meron lattice in chiral magnet Co8Zn9Mn3 raises the immediate challenging question that whether a single meron pair, which is the most fundamental topological structure in any 2D meron systems, can be created and stabilized in a continuous FM film? Utilizing winding number conservation, we develop a new method to create and stabilize a single pair of merons in a continuous Py film by local vortex imprinting from a Co disk. By observing the created meron pair directly within a magnetic field, we determine its topological structure unambiguously and explore the topological effect in its creation and annihilation processes. Our work opens a pathway towards developing and controlling topological structures in general magnetic systems without the restriction of perpendicular anisotropy and Dzyaloshinskii–Moriya interaction.

Meron excitations in theν=1quantum Hall bilayer and the plasma analogy

We study meron quasiparticle excitations in the $\ensuremath{\nu}=1$ quantum Hall bilayer. Considering the well-known single meron state, we introduce its effective form, valid in the long-distance limit. That enables us to propose two (and more) meron states in the same limit. Further, establishing a plasma analogy of the (111) ground state, we find the impurities that play the role of merons and derive meron charge distributions. Using the introduced meron constructions in generalized (mixed) ground states and corresponding plasmas for arbitrary distance between the layers, we calculate the interaction between the construction implied impurities. We also find a correspondence between the impurity interactions and meron interactions. This suggests a possible explanation of the deconfinement of the merons recently observed in the experiments.

Meron Pseudospin Solutions in Quantum Hall Systems

In this paper we report calculations of some pseudospin textures for bilayer quantum hall systems with filling factor ν=1. The textures we study are isolated single meron solutions. Meron solutions have already been studied at great length by others by minimising the microscopic Hamiltonian between microscopic trial wavefunctions. Our approach is somewhat different. We calculate them by numerically solving the nonlinear integro-differential equations arising from extremisation of the effective action for pseudospin textures. Our results can be viewed as augmenting earlier results and providing a basis for comparison. Our differential equation approach also allow us to dilineate the impact of different physical effects like the pseudospin stiffness and the capacitance energy on the meron solution.

Minkowski space Yang–Mills fields from solutions of equations in the three-dimensional Euclidean space

Equations in the three-dimensional Euclidean space are derived by combining the Yang–Mills field equations with the conditions which are imposed on a Yang–Mills field in Bernreuther’s method of constructing Yang–Mills fields in Minkowski space from Yang–Mills fields in Euclidean space. By a proper ansatz for the Yang–Mills fields these equations are reduced to a single differential equation. The differential equation is identical with merons’ equation in Euclidean space if we consider solutions of the latter equation which are functions of the ratio t/ρ, where t is the Euclidean time and ρ is the three-dimensional radius. One such solution is the single meron solution in Euclidean space. Starting from this and applying the method we get the de Alfaro–Fubini–Furlan solution in Minkowski space. Then, a more general ansatz is considered, which leads to a system of three nonlinear differential equations.

Elliptic generalization of the one-meron configuration

Solutions of the SU(2) Yang-Mills equations are obtained by solving D'Alembertianpsi+lambdapsi/sup 3/=0. We exhibit generalized solutions psi=E (u)/r which become the single meron when the parameter k for the elliptic function E (u) tends to zero.

Deformations and spectral properties of merons

We consider a meron–antimeron pair located at a, b, ∈ R4, and show that the spectrum of its stability operator is not bounded below [in precise mathematical terms: The stability operator defined on C∞0(R4−{a,b}) has a self-adjoint extension, possibly many, all of which are unbounded below]. We regularize a single meron located at the origin by replacing it inside a sphere of radius R0 and outside a sphere of radius R by ’’half instantons,’’ and show that for R≫R0 the regularized configuration continues to be unstable. For R0 finite and R=∞, we show that the spectrum of the stability operator continues to extend to −∞. We employ a singular transformation to embed R4 into S3×R where the meron pair takes a simple form and its stability operator ℒ becomes ℒ=−d2/dτ2+V, where τ∈R, and the potential V can be diagonalized in terms of the angular momenta, spin, and isospin of the vector field. The spectrum of ℒ is continuous and extends from −2 to +∞. We determine the number of (generalized) zero eigenmodes of ℒ, and calculate its spectrum explicitly.

Single meron configuration in transverse gauge

The Alfaro-Fubini-Furlan single meron configuration for SU(2) Yang-Mills theory is studied in the transverse gauge. It is shown that, as the euclidean time varies from distant past to distant future, this configuration evolves from the supervacuum to the Gribov vacuum which is the nonsingular vacuum with the topological charge 1 2 .