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）
Alberto Alonso-Izquierdo, Maximilian Bachmaier, Andrzej Wereszczynski
We analyze how the geodesic motion in the 3- and 4-vortex sectors of the Abelian-Higgs model at critical coupling is deformed by the excitation of a massive bound mode. We find that the geodesics corresponding to BPS solutions with enhanced symmetry remain unchanged, although the direction of the actual motion depends on the mode-generated force, i.e., a force arising from the change of the mode frequency along the geodesic. In a generic case, for example in head-on collisions between the axially symmetric 1- and 2-vortex or between two 2-vortices, the vortex trajectories can differ strongly from the BPS geodesic. This enhances the chaotic behavior in the formation of the final state.
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 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.
We investigate an action which resembles the effective action of brane-antibrane system derived from boundary string field theory. We find that the action has smooth vortex solutions which saturate the Bogomol'nyi bound.
Moduli space dynamics of multi-D-vortices from D2${\bar {\rm D}}$ (equivalently, parallel straight D-strings from D3${\bar {\rm D}}$3) is systematically studied. For the BPS D-vortices, we show through exact calculations that the classical motion of randomly-distributed $n$ D-vortices is governed by a relativistic Lagrangian of free massive point-particles. When the head-on collision of two identical BPS D-vortices of zero radius is considered, it predicts either 90${}^{\circ}$ scattering or 0${}^{\circ}$ scattering equivalent to 180${}^{\circ}$ scattering. Since the former leads to a reconnec…
We construct exact vortex solutions to the equations of motion of the Abelian Higgs model defined in non commutative space, analyzing in detail the properties of these solutions beyond the BPS point. We show that our solutions behave as smooth deformations of vortices in ordinary space time except for parity symmetry breaking effects induced by the non commutative parameter $θ$.
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 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 implica…
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 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 study N=1 supersymmetric gauge theories coupled with higher derivative chiral models in four dimensions in the off-shell superfield formalism. We solve the equation of motion for the auxiliary fields and find two distinct on-shell structures of the Lagrangian that we call the canonical and non-canonical branches characterized by zero and non-zero auxiliary fields, respectively. We classify BPS states of the models in Minkowski and Euclidean spaces. In Minkowski space, we find Abelian and non-Abelian vortices, vortex-lumps (or gauged lumps with fractional lump charges) as 1/2 BPS states in t…
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)）
We introduce some techniques for making a more global analysis of the existence of geodesics on a Seiberg-Witten Riemann surface with metric $ds^2 = |λ_{SW}|^2$. Because the existence of such geodesics implies the existence of BPS states in N=2 supersymmetric Yang-Mills theory, one can use these methods to study the BPS spectrum in various phases of the Yang-Mills theory. By way of illustration, we show how, using our new methods, one can easily recover the known results for the N=2 supersymmetric SU(2) pure gauge theory, and we show in detail how it also works for the N=2, SU(2) theory couple…
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…
Conformal mapping techniques are used to determine analytically the geodesics on the Seiberg-Witten Riemann surface which correspond to the BPS dyon states in N=2 SUSY QCD with gauge group SU(2) and up to three flavors of massless fundamental matter. The results are exact for zero and two flavors, and approximate in the weak-coupling limit for one and three flavors. The presence of states of magnetic charge 2, in the three-flavor case only, is confirmed.
We review recent results on the BPS multi-wall solutions in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C) hypermultiplets in the fundamental representation. Total moduli space of the BPS non-Abelian walls is found to be the complex Grassmann manifold SU(N_F)/[SU(N_C)xSU(N_F-N_C)xU(1)]. Exact solutions are obtained with full generic moduli for infinite gauge coupling. A 1/4 BPS equation is also solved, giving vortices together with the non-Abelian walls and monopoles in the Higgs phase attached to the vortices. The full moduli space of the 1/4 BPS solutions is found to …
The AdS/CFT correspondence between Sasaki-Einstein spaces and quiver gauge theories is studied from the perspective of massless BPS geodesics. The recently constructed toric Lpqr geometries are considered: we determine the dual superconformal quivers and the spectrum of BPS mesons. The conformal anomaly is compared with the volumes of the manifolds. The U(1)^2_F x U(1)_R global symmetry quantum numbers of the mesonic operators are successfully matched with the conserved momenta of the geodesics, providing a test of AdS/CFT duality. The correspondence between BPS mesons and geodesics allows to …
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 relate a number of results in the theory of flat surfaces to BPS spectra of a class of 4d $\mathcal{N}=2$ supersymmetric quantum field theories arising from M5 branes wrapped on Riemann surfaces -- $A_1$ class S theories. In particular, we apply classic results of Eskin and Masur, which determine the asymptotic growth of geodesic counts at large length on flat surfaces, as well as more recent progress in the mathematics literature, to determine the large mass asymptotics of the BPS spectra of a wide class of such theories at generic points in the Coulomb branch.
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 review recent results on solitons in supersymmetric (SUSY) non-Abelian gauge theories, focusing on our papers: hep-th/0405194, hep-th/0405129, and hep-th/0404198. We construct the BPS multi-wall solutions in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C) hypermultiplets in the fundamental representation. Exact solutions are obtained with full generic moduli for infinite gauge coupling. Total moduli space of the BPS non-Abelian walls is found to be the complex Grassmann manifold SU(N_F) / [SU(N_C)\times SU(N_F-N_C) \times U(1)]. A 1/4 BPS equation is also studied whic…
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…
We study the tension of vortices in N=2 SQCD broken to N=1 by a superpotential W(Φ), in color-flavor locked vacua. The tension can be written as T = T_{BPS} + T_{non BPS}. The BPS tension is equal to 4π|\T| where we call \T the holomorphic tension. This is directly related to the central charge of the supersymmetry algebra. Using the tools of the Cachazo-Douglas-Seiberg-Witten solution we compute the holomorphic tension as a holomorphic function of the couplings, the mass and the dynamical scale: \T = \sqrt{W'^2+f}. A first approximation is given using the generalized Konishi anomaly in the se…
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.
N=2 SQED with several flavors admits multiple, static BPS domain wall solutions. We determine the explicit two-kink metric and examine the dynamics of colliding domain walls. The multi-kink metric has a toric Kahler structure and we reduce the Kahler potential to quadrature. In the second part of this paper, we consider semi-local vortices compactified on circle. We argue that, in the presence of a suitable Wilson line, the vortices separate into domain wall constituents. These play the role of fractional instantons in two-dimensional gauge theories and sigma-models.
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.
We study the stability of non-Abelian semi-local vortices based on an N=2 supersymmetric H = [SU(Nc) x U(1)]/Z_Nc = U(Nc) gauge theory with an arbitrary number of flavors (Nf > Nc) in the fundamental representation, when certain N=1 mass terms are present, making the vortex solutions no longer BPS-saturated. Local (ANO-like) vortices are found to be stable against fluctuations in the transverse directions. Strong evidence is found that the ANO-like vortices are actually the true minima. In other words, the semi-local moduli, which are present in the BPS limit, disappear in our non-BPS system, …
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…
The abelian Higgs model on the noncommutative plane admits both BPS vortices and non-BPS fluxons. After reviewing the properties of these solitons, we discuss several new aspects of the former. We solve the Bogomoln'yi equations perturbatively, to all orders in the inverse noncommutivity parameter, and show that the metric on the moduli space of k vortices reduces to the computation of the trace of a k-dimensional matrix. In the limit of large noncommutivity, we present an explicit expression for this metric.
We study supersymmetric probe M5-branes in the AdS_4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M_3. This amounts to introducing internal defects within the framework of the 3d-3d correspondence. The BPS condition for a probe M5-brane extending along all of AdS_4 requires it to wrap a surface embedded in an S^2-fibration over M_3. We find that the projection of this surface to M_3 can be either a geodesic or a tubular surface around a geodesic. These configurations preserve an extra U(1) symmetry, in addition to the one corresponding to the R-symmetry of the dual 3d…
We study 1/2 BPS domain walls, 1/2 BPS flux tubes (strings) and their 1/4 BPS junctions. We consider the simplest example of N=2 Abelian gauge theory with two charged matter hypermultiplets which contains all of the above-listed extended objects. In particular, we focus on string-wall junctions (boojums) and calculate their energy. It turns out to be logarithmically divergent in the infrared domain. We compute this energy first in the (2+1)-dimensional effective theory on the domain wall and then, as a check, obtain the same result from the point of view of (3+1)-dimensional bulk theory. Next,…
In earlier work with N. Seiberg, we explored connections between monopole operators, the Coulomb branch modulus, and vortices for 3d, N=2 supersymmetric, $U(1)_k$ Chern-Simons matter theories. We here extend the monopole / vortex matching analysis, to theories with general matter electric charges. We verify, for general matter content, that the spin and other quantum numbers of the chiral monopole operators match those of corresponding BPS vortex states, at the top and bottom of the tower associated with quantizing the vortices' Fermion zero modes. There are associated subtleties from non-norm…
We study BPS saturated objects with axial geometry (wall junctions, vortices) in generalized Wess-Zumino models. It is observed that the tension of such objects is negative in general (although ``exceptional'' models are possible). We show how an ambiguity in the definition of central charges does not affect physical quantities, and we comment on the stability of the junctions and vortices. We illustrate these issues in two classes of models with Z_N symmetry. On the basis of analytical large N calculations and numerical calculations at finite N, we argue that the domain wall junctions in thes…
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on noncommutative spaces R^{2n}_theta x G/H which are manifestly G-symmetric. Given a G-representation, by twisting with a particular bundle over G/H, we obtain a G-equivariant U(k) bundle with a G-equivariant connection over R^{2n}_theta x G/H. The U(k) Donaldson-Uhlenbeck-Yau equations on these spaces reduce to vortex-type equations in a particular quiver gauge theory on R^{2n}_theta. Seiberg-Witten monopole equations are particular examples. The noncommutative BPS configurations are formulated with partial isometrie…
We consider equivariant dimensional reduction of Yang-Mills theory on K"ahler manifolds of the form M times CP^1 times CP^1. This induces a rank two quiver gauge theory on M which can be formulated as a Yang-Mills theory of graded connections on M. The reduction of the Yang-Mills equations on M times CP^1 times CP^1 induces quiver gauge theory equations on M and quiver vortex equations in the BPS sector. When M is the noncommutative space R_theta^{2n} both BPS and non-BPS solutions are obtained, and interpreted as states of D-branes. Using the graded connection formalism, we assign D0-brane ch…
We construct non-extremal as well as extremal black string solutions in minimal five-dimensional supergravity coupled to vector multiplets using dimensional reduction to three Euclidean dimensions. Our method does not assume that the scalar manifold is a symmetric space, and applies as well to a class of non-supersymmetric theories governed by a generalization of special real geometry. We find that five-dimensional black string solutions correspond to geodesics in a specific totally geodesic para-Kähler submanifold of the scalar manifold of the dimensionally reduced theory, and identify the su…
Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted Σ_{n,m}, are spaces of C_n-invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N-n coincident vortices at the polygon's centre. The geometric properties of Σ_{n,m} are investigated, and it is found that Σ_{n,n-1} is isometric to the hyperbolic plane of curvature -1/(3πn). Geodesic flow on Σ_{n,m}, and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong, are analyzed in det…
Interactions between non-BPS non-Abelian vortices are studied in non-Abelian U(1) x SU(N) extensions of the Abelian-Higgs model in four dimensions. The distinctive feature of a non-Abelian vortex is the presence of an internal CP^{N-1} space of orientational degrees of freedom. For fine-tuned values of the couplings, the vortices are BPS and there is no net force between two static parallel vortices at arbitrary distance. On the other hand, for generic values of the couplings the interactions between two vortices depend non-trivially on their relative internal orientations. We discuss the prob…
We construct the effective theory of intersecting branes and investigate the BPS monopoles in the theory. The monopoles obtained are the generalization of Nielsen-Olesen vortex. We study the properties of the solutions and interpret them as the D0-branes on the brane-intersections.
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 exploit the relationship between the space components of the energy-momentum tensor and the supercurrent to discuss the connection between the BPS equations and the vanishing of the components of the stress tensor in various supersymmetric theories with solitons. Using the fact that certain combination of supercharges annihilate BPS states, we show that $T_{ij}=0$ for kinks, vortices and dyons, displaying the connection between supersymmetry and non-interacting BPS solitons.
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…
