11 pages, 4 figures. To appear in the proceedings of APCTP Winter School on Black Hole Astrophysics 2008, Daejeon and Pohang, Korea, 24-29 January, 2008. Submitted to J. Korean Phys. Soc
We investigate the BPS configuration of the multi D-vortices produced from the D2${\bar {\rm D}}$2 system. Based on the DBI-type action with a Gaussian-type runaway potential for a complex tachyon field, the BPS limit is achieved when the tachyon profile is thin. The solution states randomly-distributed $n$ static D-vortices with zero interaction. With the obtained BPS configuration, we derive the relativistic Lagrangian which describes the dynamics of free massive D-vortices. We also discuss the 90${}^{\circ}$ and 180${}^{\circ}$ scattering of two identical D-vortices, and present its implications on the reconnection in the dynamics of cosmic superstrings.
We develop a new method for obtaining the BPS equations of static vortices motivated by the results of the \textit{On-Shell} method on the standard Maxwell-Higgs model and its Born-Infeld-Higgs model~\cite{Atmaja:2014fha}. Our method relies on the existence of what we shall call an energy function, $Q$, which is a mere function of the (effective) fields. The total energy of BPS vortices, $E_{BPS}$, are simply given by a difference between the boundaries value of $Q$ at $r\to\infty$ and at $r=0$, $E_{BPS}=Q(r\to\infty)-Q(r=0)$. Imposing a condition that these (effective) fields are independent,…
We investigate the vortex-type BPS equations in the ABJM theory without and with mass-deformation. We systematically classify the BPS equations in terms of the number of supersymmetry and the R-symmetries of the undeformed and mass-deformed ABJM theories. For the undeformed case, we analyze the ${\cal N}=2$ BPS equations for U(2)$\times$U(2) gauge symmetry and obtain a coupled differential equation which can be reduced to either Liouville- or Sinh-Gordon-type vortex equations according to the choice of scalar functions. For the mass-deformed case with U($N$)$\times$U($N$) gauge symmetry, we ob…
In this paper the zero modes of fluctuation of cylindrically symmetric self-dual vortices are analyzed and described in full detail. These BPS topological defects arise at the critical point between Type II and Type I superconductors, or, equivalently, when the masses of the Higgs particle and the vector boson in the Abelian Higgs model are equal. In addition, novel bound states of Higss and vector bosons trapped by the self-dual vortices at their core are found and investigated.
We explore the low-energy dynamics of 1/2-BPS heavy particles coupled to the ABJM model via the Higgsing of M2-branes, with focus on physical understanding of the recently discovered 1/2-BPS Wilson loop operators. The low-energy theory of 1/2-BPS heavy particles turns out to have the U(N|N) supergauge symmetry, which explains the novel structure of the 1/2-BPS Wilson loop operator as a holonomy of a U(N|N) superconnection. We show that the supersymmetric transformation of the Wilson loop operator can be identified as a fermionic supergauge transformation, which leads to their invariance under …
We have analyzed Maxwell-Chern-Simons-Higgs BPS vortices in a Lorentz-violating CPT-odd context. The Lorentz violation induces profiles with a conical behavior at the origin. For some combination of the coefficients for Lorentz violation there always exists a sufficiently large winding number for which the magnetic field flips its sign.
We present several analytical solutions of BPS vortices and monopoles in the generalized Abelian Maxwell-Higgs and Yang-Mills-Higgs theories, respectively. These models have recently been extensively studied and several exact solutions have already been obtained in \cite{Casana:2014qfa, Casana:2013lna}. In each theory, the dynamics is controlled by the additional two positive scalar-field-dependent functions, $f(|ϕ|)$ and $w(|ϕ|)$. For the case of vortices, we work in the ordinary symmetry-breaking Higgs potential, while for the case of monopoles we have the ordinary condition of the Prasad-So…
In this paper zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged $\mathbb{U}(1)$ nonlinear $\mathbb{CP}^1$-model. If $2πn$, $n\in \mathbb{Z}$, is the quantized magnetic flux of the two species of BPS vortex solutions, $2n$ linearly independent vortex zero modes for each species are found and described. The existence of two species of moduli spaces of dimension $2n$ of these stringy topological defects is thus locally shown.
We study BPS vortices in the mass-deformed non-relativistic ${\C N}=6$ $U(N)_k\times U(N)_{-k}$ Chern-Simons-matter theory. We focus on the massive deformation that preserves the maximal ${\C N}=6$ supersymmetry, and consider a non-relativistic limit that carry 14 supercharges. In this non-relativistic field theory we find Jackiw-Pi type exact vortex solutions combined with $S^3$ fuzzy sphere geometry. We analyse their properties and show that they preserve one dynamical, one conformal and five kinematical supersymmetries among the full super Schrödinger symmetry.
In this work, we propose a class of SU(N) Yang-Mills models, with adjoint Higgs fields, that accept BPS center vortex equations. The lack of a local magnetic flux that could serve as an energy bound is circumvented by including a new term in the energy functional. This term tends to align, in the Lie algebra, the magnetic field and one of the adjoint Higgs fields. Finally, a reduced set of equations for the center vortex profile functions is obtained (for N=2,3). In particular, Z(3) BPS vortices come in three colours and three anticolours, obtained from an ansatz based on the defining represen…
We consider vortices in scalar electrodynamics and compute the leading quantum correction to their energies for the BPS case of identical classical masses of the Higgs and gauge fields. In particular, we focus on the winding number $n$ dependence of these corrections, from which we can extract the binding energies of configurations with larger $n$. For both dimensionalities, $D=2+1$ and $D=3+1$, we find that quantum corrections are negative and scale approximately linearly with $n$, so that combined vortices are favored over isolated ones.
From BPS geodesics to mode-driven dynamics in the scattering of multiple BPS vortices
University of Salamanca（萨拉曼卡大学）；Ludwig-Maximilians-Universität（慕尼黑大学）；Max-Planck-Institut fur Physik（马克斯·普朗克物理研究所）；Jagiellonian University（雅盖隆大学）；Hiroshima University（广岛大学）
The BPS baby Skyrme models are submodels of baby Skyrme models, where the nonlinear sigma model term is suppressed. They have skyrmion solutions saturating a BPS bound, and the corresponding static energy functional is invariant under area-preserving diffeomorphisms (APDs). Here we show that the solitons in the BPS baby Skyrme model, which carry a nontrivial topological charge $Q_{b} \in π_2(S^2)$ (a winding number), are dual to vortices in a BPS vortex model with a topological charge $Q_{v}\in π_1(S^1)$ (a vortex number), in the sense that there is a map between the BPS solutions of the two m…
We demonstrate for the first the existence of electrically charged BPS vortices in a Maxwell-Higgs model supplemented with a parity-odd Lorentz-violating (LV) structure belonging to the CPT-even gauge sector of the standard model extension and a fourth order potential (in the absence of the Chern-Simons term). The modified first order BPS equations provide charged vortex configurations endowed with some interesting features: localized and controllable spatial thickness, integer flux quantization, electric field inversion and localized magnetic flux reversion. This model could possibly be appli…
University of Salamanca（萨拉曼卡大学）；School of Mathematics, Statistics and Actuarial Sciences, University of Kent（肯特大学数学、统计与精算科学学院）；Institute of Theoretical Physics, Jagiellonian University（雅盖隆大学理论物理研究所）；International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2)（结型手性超材料可持续发展国际研究所 (WPI-SKCM2)）
In this paper we show how to derive the Bogomolny's equations of the generalized self-dual Maxwell-Chern-Simons-Higgs model presented in \cite{Bazeia:2012ux} by using the BPS Lagrangian method with a particular choice of the BPS Lagrangian density. We also show that the identification, potential terms, and Gauss's law constraint can be derived rigorously under the BPS Lagrangian method. In this method, we find that the potential terms are the most general form that could have the BPS vortex solutions. The Gauss's law constraint turns out to be the Euler-Lagrange equations of the BPS Lagrangian…
We investigate the existence of first-order vortices inherent to both the Maxwell-Chern-Simons-Higgs and the Maxwell-Chern-Simons-$CP(2)$ models extended via the inclusion of an extra scalar sector which plays the role of a source field. For both cases, we focus our attention on the time-independent configurations with radial symmetry which can be obtained through the implementation of the so-called Bogomol'nyi-Prasad-Sommerfield (BPS) prescription. In this sense, in order to solve the corresponding first-order differential equations, we introduce some particular scenarios which are driven by …
We have investigated and verified the existence of stable uncharged Bogomol'nyi-Prasad-Sommerfeld (BPS) vortices in the framework of an Abelian Maxwell-Higgs model supplemented with CPT-even and Lorentz-violating (LV) terms belonging to the gauge and Higgs sectors of the standard model extension. The analysis is performed in two situations: first, one by considering the Lorentz violation only in the gauge sector and then in both gauge and Higgs sectors. In the first case, it is observed that the model supports vortices somehow equivalent to the ones appearing in a dielectric medium. The Lorent…
We have established a prescription for the calculation of analytical vortex solutions in the context of generalized Maxwell-Higgs models whose overall dynamics is controlled by two positive functions of the scalar field. We have also determined a natural constraint between these functions and the Higgs potential allowing the existence of axially symmetric Bogomol'nyi-Prasad-Sommerfield (BPS) solutions possessing finite energy. Furthermore, when the generalizing functions are chosen suitably, the nonstandard BPS equations can be solved exactly. We have studied some examples, comparing them with…
In this article we show that the new BPS equations for vortices, with nonzero diagonal components of the stress tensor, obtained in \cite{Atmaja:2015lia} for the generalized Maxwell-Higgs model can also be derived using the BPS Lagrangian method developed in \cite{Atmaja:2015umo}. We add into the original BPS Lagrangian $L_{BPS}=\int dQ$, which is a total derivative term, two additional terms that are proportional to square of the first-derivative of scalar effective field, $f'(r)^2$, and to a function that depends only on the scalar effective field. These additional terms produce additional c…
There has been some recent interest in the study of non-abelian BPS monopoles in the limit of large magnetic charge. Most investigations have used a magnetic bag approximation, in which spherical symmetry is assumed within an abelian description. In particular, this approach has been used to suggest the existence of two types of magnetic bag, with differing distributions of the zeros of the Higgs field, together with multi-layer structures, containing several magnetic bags. This paper is concerned with the analogous situation of abelian BPS vortices in the hyperbolic plane, in the limit of lar…
In this note we investigate bound states, where scalar and vector bosons are trapped by BPS vortices in the Abelian Higgs model with a critical ratio of the couplings. A class of internal modes of fluctuation around cylindrically symmetric BPS vortices is characterized mathematically, analysing the spectrum of the second-order fluctuation operator when the Higgs and vector boson masses are equal. A few of these bound states with low values of quantized magnetic flux are described fully, and their main properties are discussed.
We have performed a complete study of BPS vortex solutions in the Abelian sector of the standard model extension (SME). Specifically, we have coupled the SME electromagnetism with a Higgs field which is supplemented with a Lorentz-violating CPT-even term. We have verified that Lorentz violation (LV) belonging to the Higgs sector allows to interpolate between some well known models like, Maxwell-Higgs, Chern-Simons-Higgs and Maxwell-Chern-Simons-Higgs. We can also observed that the electrical charged density distribution is nonnull in both CPT-even and CPT-odd models; however, the total electri…
We show that vortices of Yang-Mills-Higgs model in $R^{2}$ space can be regarded as instantons of Yang-Mills model in $R^{2}\times Z_{2}$ space. For this, we construct the noncommutative $Z_{2}$ space by explicitly fixing the $Z_{2}$ coordinates and then show, by using the $Z_{2}$ coordinates, that BPS equation for the vortices can be considered as a self-dual equation. We also propose the possibility to rewrite the BPS equations for vortices as ADHM equations through the use of self-dual equation.
Effects of mass deformations on 1/2 Bogomol'nyi-Prasad-Sommerfield (BPS) non-Abelian vortices are studied in 4d N=2 supersymmetric U(1) \times SO(2n) and U(1) \times USp(2n) gauge theories, with Nf=2n quark multiplets. The 2d N=(2,2) effective worldsheet sigma models on the Hermitian symmetric spaces SO(2n)/U(n) and USp(2n)/U(n) found recently which describe the low-energy excitations of the orientational moduli of the vortices, are generalized to the respective massive sigma models. The continuous vortex moduli spaces are replaced by a finite number (2^{n-1} or 2^{n}) of vortex solutions. The…
在非对易空间R^{2n}_theta x G/H上构造了Yang-Mills方程的显式BPS解和非BPS解.给定一个G-表示，通过对G/H上的一个特殊丛进行扭曲，得到了R^{2n}_theta x G/H上的一个G-等变联络的G-等变U（k）丛.这些空间上的U（k）Donaldson-Uhlenbeck-Yau方程在R^{2n}_θ上的特殊规范规范理论中化为涡旋型方程。Seiberg-Witten方程是一个特殊的例子。非对易BPS组态的部分等距，这是从一个等变的Atiyah-Bott-Shapiro建设制定。它们可以被解释为充满空间的膜-反膜系统中的D 0-膜。
The Omega-deformation is a harmonic trap, penning certain excitations near the origin in a manner consistent with supersymmetry. Here we explore the dynamics of BPS monopoles and vortices in such a trap. We pay particular attention to monopoles in the Higgs phase, when they are confined to a vortex string. Unusually for BPS solitons, the mass of these confined monopoles is quadratic in the topological charges. We compute an index theorem to determine the number of collective coordinates of confined monopoles. Despite being restricted to move on a line, we find that they have a rich dynamics. A…
We discuss a supersymmetric extension of a non-relativistic Chern-Simons matter theory, known as the SUSY Jackiw-Pi model, in a harmonic trap. We show that the non-relativistic version of the superconformal symmetry, called the super-Schrödinger symmetry, is not spoiled by an external field including the harmonic potential. It survives as a modified symmetry whose generators have explicit time dependences determined by the strength of the trap, the rotation velocity of the system and the fermion number chemical potential. We construct 1/3 BPS states of trapped Jackiw-Pi vortices preserving a p…
We study the partition functions of BPS vortices and magnetic monopole operators, in gauge theories describing $N$ M2-branes. In particular, we explore two closely related methods to study the Cardy limit of the index on $S^2\times\mathbb{R}$. The first method uses the factorization of this index to vortex partition functions, while the second one uses a continuum approximation for the monopole charge sums. Monopole condensation confines most of the $N^2$ degrees of freedom except $N^{\frac{3}{2}}$ of them, even in the high temperature deconfined phase. The resulting large $N$ free energy stat…
