In this paper we derive the universal R-matrix for the Yangian Y(u(2|2)), which is an abstract algebraic object leading to rational solutions of the Yang-Baxter equation on representations. We find that on the fundamental representation the universal R-matrix reduces to the standard rational R-matrix R = R_0(1 + P/u), where the scalar prefactor is surprisingly simple compared to prefactors one finds e.g. for sl(n) R-matrices. This leads precisely to the S-matrix giving the Bethe Ansatz of one-loop N = 4 Super Yang-Mills theory and two-loop N = 6 Chern-Simons theory.
We propose a generating function for scattering amplitudes of N=6 super-Chern-Simons theory which parallels a recent work on N=4 super-Yang-Mills theory by Arkani-Hamed et al. Our result suggests that the scattering amplitudes of the super-Chern-Simons theory exhibit Yangian invariance.
Recent developments in the determination of the planar S-matrix of N=4 Super Yang-Mills are closely related to its Yangian symmetry. Here we provide evidence for a yet unobserved additional symmetry: the Yangian level-one helicity operator.
We will discuss an integrable structure for weakly coupled superconformal Yang-Mills theories, describe certain equivalences for the Yangian algebra, and fill a technical gap in our previous study of this subject.
The existence of a "bonus" U(1) level-one Yangian symmetry of N=4 super-Yang-Mills has recently been proposed. We provide evidence for this proposal by constructing the BRST-invariant nonlocal charge in the pure spinor sigma model corresponding to this bonus level-one symmetry. We also construct analogous charges for bonus U(1) symmetries at all odd levels of the Yangian.
In this article we establish the notion of classical Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory and for related planar gauge theories. After revisiting Yangian invariance for the equations of motion, we describe how the bi-local generators act on the action of the model such that the latter becomes exactly invariant. In particular, we elaborate on the relevance of the planar limit and how to act non-linearly with bi-local generators on the cyclic action.
It is known that the Yangian of PSU(2,2|4) is a symmetry of the tree-level S-matrix of N=4 super Yang-Mills. On the other hand, the complete one-loop dilatation operator in the same theory commutes with the level-one Yangian generators only up to certain boundary terms found by Dolan, Nappi and Witten. Using a result by Zwiebel, we show how the Yangian symmetry of the tree-level S-matrix of N=4 super Yang-Mills implies precisely the Yangian invariance, up to boundary terms, of the one-loop dilatation operator.
We conjecture that every rational Yangian invariant in N=4 SYM theory satisfies a recently introduced notion of cluster adjacency. We provide evidence for this conjecture by using the Sklyanin Poisson bracket on Gr(4,n) to check numerous examples.
We investigate Yangian invariance of deformed on-shell diagrams with D=4, N=4 superconformal symmetry. We find that invariance implies a direct relationship between the deformation parameters and the permutation associated to the on-shell graph. We analyse the connection with deformations of scattering amplitudes in N=4 super-Yang-Mills theory and the possibility of using the deformation parameters as a regulator preserving Yangian invariance. A study of higher-point tree and loop graphs suggests that manifest Yangian invariance of the amplitude requires trivial deformation parameters.
In this paper we review recent results on symmetries in N=4 super Yang-Mills theory. Symmetries are of invaluable help in studying and constraining the scattering amplitudes, and there has been a lot of progress in recent years concerning this topic. It has been realised that the ordinary superconformal symmetry is not the full symmetry of this theory. There is indeed a dual superconformal symmetry, and together they form a Yangian structure, pointing to the underlying integrability of the theory. Here we give an overview of the Yangian algebra and of its action on the scattering amplitudes, a…
Tree-level scattering amplitudes in N=4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a 'dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action of the dual superconformal generators in on-shell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,2|4) symmet…
We show that appropriately supersymmetrized smooth Maldacena-Wilson loop operators in N=4 super Yang-Mills theory are invariant under a Yangian symmetry Y[psu(2,2|4)] built upon the manifest superconformal symmetry algebra of the theory. The existence of this hidden symmetry is demonstrated at the one-loop order in the weak coupling limit as well as at leading order in the strong coupling limit employing the classical integrability of the dual AdS_5 x S^5 string description. The hidden symmetry generators consist of a canonical non-local second order variational derivative piece acting on the …
Recently it has been argued that tree-level scattering amplitudes in N=4 Yang-Mills theory are uniquely determined by a careful study of their superconformal and Yangian symmetries. However, at one-loop order these symmetries are known to become anomalous due to infrared divergences. We compute these one-loop anomalies for amplitudes defined through dimensional regularisation by studying the tree-level symmetry transformations of the unitarity branch cuts, keeping track of the crucial collinear terms arising from the holomorphic anomaly. We extract the superconformal anomalies and show that th…
Constraints of the osp(6|4) symmetry on tree-level scattering amplitudes in N=6 superconformal Chern-Simons theory are derived. Supplemented by Feynman diagram calculations, solutions to these constraints, namely the four- and six-point superamplitudes, are presented and shown to be invariant under Yangian symmetry. This introduces integrability into the amplitude sector of the theory.
In this paper we analyse formulas which reproduce different contributions to scattering amplitudes in N=4 super Yang-Mills theory through a Grassmannian integral. Recently their Yangian invariance has been proved directly by using the explicit expression of the Yangian level-one generators. The specific cyclic structure of the form integrated over the Grassmannian enters in a crucial way in demonstrating the symmetry. Here we show that the Yangian symmetry fixes this structure uniquely.
Quantum gravity in AdS$_7 \times$S$^4$ is dual to a 6d superconformal field theory, known as the 6d $(2,0)$ theory, which is very challenging to describe because it lacks a conventional Lagrangian description. On the other hand, certain null reductions of the 6d $(2,0)$ theory give rise to 5d Lagrangian theories with $SU(1,3)$ spacetime symmetry, $SO(5)$ R-symmetry, and 24 supercharges. This appears to be closely related to the superconformal group of a 3d superconformal Chern-Simons theory known as the ABJM theory, which is believed to be integrable in the planar limit, if one exchanges the r…
We demonstrate that the planar real-$β$-deformed Super-Yang--Mills theory possesses an infinitely-dimensional Yangian symmetry algebra and thus is classically integrable. This is achieved by the introduction of the twisted coproduct which allows us to lift the apparent $\mathcal{N}=1$ supersymmetry first to the full $\mathcal{N}=4$ symmetry of the parent $\mathcal{N} = 4$ SYM theory, and subsequently to its Yangian.
We demonstrate that the four and six-point tree-level amplitudes of N=6 superconformal Chern-Simons theory (ABJM) enjoy OSp(6|4) dual superconformal symmetry if one enlarges the dual superspace to include three additional Grassmann-even coordinates which correspond to an abelian isometry of CP3. The inclusion of these coordinates enables us to match the nontrivial dual superconformal generators with level-one Yangian generators when acting on on-shell amplitudes. We also discuss some implications of dual conformal symmetry for loop-level amplitudes.
We review recent progress in the understanding of symmetries for scattering amplitudes in N=4 superconformal Yang-Mills theory. It is summarized how the superficial breaking of superconformal symmetry by collinear anomalies and the renormalization process can be cured at tree and loop level. This is achieved by correcting the representation of the superconformal group on amplitudes. Moreover, we comment on the Yangian symmetry of scattering amplitudes and how it inherits these correction terms from the ordinary Lie algebra symmetry. Invariants under this algebra and their relation to the Grass…
We classify the rational Yangian invariants of the $m=2$ toy model of $\mathcal{N}=4$ Yang-Mills theory in terms of generalised triangles inside the amplituhedron $\mathcal{A}_{n,k}^{(2)}$. We enumerate and provide an explicit formula for all invariants for any number of particles $n$ and any helicity degree $k$. Each invariant manifestly satisfies cluster adjacency with respect to the $Gr(2,n)$ cluster algebra.
We show that a certain class of light-like Wilson loops exhibits a Yangian symmetry at one loop, or equivalently, in an Abelian theory. The Wilson loops we discuss are equivalent to one-loop MHV amplitudes in N=4 super Yang-Mills theory in a certain kinematical regime. The fact that we find a Yangian symmetry constraining their functional form can be thought of as the effect of the original conformal symmetry associated to the scattering amplitudes in the N=4 theory.
Planar N=4 supersymmetric Yang-Mills theory appears to be perturbatively integrable. This work reviews integrability in terms of a Yangian algebra and compares the application to the problems of anomalous dimensions and scattering amplitudes.
In this letter we establish Yangian symmetry of planar N=4 super-Yang-Mills theory. We prove that the classical equations of motion of the model close onto themselves under the action of Yangian generators. Moreover we propose an off-shell extension of our statement which is equivalent to the invariance of the action and prove that it is exactly satisfied. We assert that our relationship serves as a criterion for integrability in planar gauge theories by explicitly checking that it applies to integrable ABJM theory but not to non-integrable N=1 super-Yang-Mills theory.
We have calculated the high spin parton splitting amplitudes postulating the Yangian symmetry of the scattering amplitudes for tensorgluons. The resulting splitting amplitudes coincide with the earlier calculations, which were based on the BCFW recursion relations. The resulting formula unifies all known splitting probabilities found earlier in gauge field theories. It describes splitting probabilities for integer and half-integer spin particles. We also checked that the splitting probabilities fulfil generalised Kounnas-Ross N=1 supersymmetry relations hinting to the fact that the underlying …
We investigate the Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory and show that its formulations in twistor and momentum twistor space can be interchanged. In particular we show that the full symmetry can be thought of as the Yangian of the dual superconformal algebra, annihilating the amplitude with the MHV part factored out. The equivalence of this picture with the one where the ordinary superconformal symmetry is thought of as fundamental is an algebraic expression of T-duality. Motivated by this, we analyse some recently proposed formulas, which reproduce differen…
We discuss the integrability structure of deformed, four-dimensional N=4 super Yang-Mills theories using Yangians. We employ a recent procedure by Beisert and Roiban that generalizes the beta deformation of Lunin and Maldacena to produce N=1 superconformal gauge theories, which have the superalgebra SU(2,2|1)xU(1)xU(1). The deformed theories, including those with the more general twist, were shown to have retained their integrable structure. Here we examine the Yangian algebra of these deformed theories. In a five field subsector, we compute the two cases of SU(2)xU(1)xU(1)xU(1) and SU(2|1)xU(…
Properties of the SO(2,n) Yangian acting on scalar and gauge fields are presented. This differential operator representation of the infinite-dimensional extension of the conformal algebra SO(2,n) is proved to satisfy the Serre relation for arbitrary spacetime dimension n for off-shell scalar theory, but only on shell and for n=4 in the gauge theory. The SO(2,n) Yangian acts simply on the off-shell kinematic invariants $(k_I+k_{I+1}+ ...)^2$, and it annihilates individual off-shell scalar $λϕ^3$ Feynman tree graphs for n=6 if the differential operator representation is extended by graph depende…
Tree-level scattering amplitudes in planar N=4 super Yang-Mills are known to be Yangian-invariant. It has been shown that integrability allows to obtain a general, explicit method to find such invariants. The uplifting of this result to the amplituhedron construction has been an important open problem. In this paper, with the help of methods proper to integrable theories, we successfully fill this gap and clarify the meaning of Yangian invariance for the tree-level amplituhedron. In particular, we construct amplituhedron volume forms from an underlying spin chain. As a by-product of this const…
Bethe ansatz equations have been proposed for the asymptotic spectral problem of AdS_4/CFT_3. This proposal assumes integrability, but the previous verification of weak-coupling integrability covered only the su(4) sector of the ABJM gauge theory. Here we derive the complete planar two-loop dilatation generator of N=6 superconformal Chern-Simons theory from osp(6|4) superconformal symmetry. For the osp(4|2) sector, we prove integrability through a Yangian construction. We argue that integrability extends to the full planar two-loop dilatation generator, confirming the applicability of the Beth…
We study Yangian-invariant deformations of scattering amplitudes in 4d N=4 supersymmetric Yang-Mills theory and 3d N=6 Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In particular, we obtain the deformed Grassmannian integral for 4d N=4 super Yang-Mills theory, both in momentum and momentum-twistor space. For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We investigate general deformations of on-shell diagrams, and find the deformed Grassmannian integral for this theory. We furthermore introduce the algebraic R-matrix construction of deformed Yangian invariants fo…
In this paper we derive in a coordinate-free manner the field equations for a lagrangean consisting of Yang-Mills kinetical term plus Chern-Simons self-coupling term. This equation turns out to be an eigenvalue equation for the covariant laplacian.
Nilpotency of the pure spinor BRST operator in a curved background implies superspace equations of motion for the background. By computing one-loop corrections to nilpotency for the heterotic sigma model, the Yang-Mills Chern-Simons corrections to the background are derived.
We consider the BPS dyonic instantons in the 5-dim supersymmetric Yang-Mills Chern-Simons theories. Its field theoretic structures and the moduli space dynamics in term of the ADHM data have been explored in detail. We find that the field theoretic Chern-Simons term leads to an effective magnetic field on instanton moduli space.
Recently, gauged supergravities in three dimensions with Yang-Mills and Chern-Simons type interactions have been constructed. In this article, we demonstrate that any gauging of Yang-Mills type with semisimple gauge group G_0, possibly including extra couplings to massive Chern-Simons vectors, is equivalent on-shell to a pure Chern-Simons type gauging with non-semisimple gauge group $G_0 \ltimes T \subset G$, where T is a certain translation group, and where G is the maximal global symmetry group of the ungauged theory. We discuss several examples.
We investigate Yangian-invariant deformations of one-loop amplitudes in N = 4 super-Yang-Mills theory employing an algebraic representation of amplitudes. In this language, we reproduce the deformed massless box integral describing the deformed four-point one-loop amplitude and compare different realizations of said amplitude.
We derive the usual first-order form of the Yang-Mills action in arbitrary dimensions by dimensional reduction from a Chern-Simons-like action. The antisymmetric tensor auxiliary field of the first-order action appears as a gauge field for the extra dimensions. The higher-dimensional geometry was introduced in our previous paper by adding dimensions "dual" to spin, as suggested by the superstring's affine Lie algebra.
We investigate finite energy solutions of Yang-Mills--Chern-Simons systems in odd spacetime dimensions, d=2n+1, with n>2. This can be carried out systematically for all n, but the cases n=3,4 corresponding to a 7,8 dimensional spacetime are treated concretely. These are static and spherically symmetric configurations, defined in a flat Minkowski background. The value of the electric charge is fixed by the Chern-Simons coupling constant.
We find wide class of exact solutions of Yang-Mills-Chern-Simons theory coupled to an external source, in terms of doubly periodic Jacobi elliptic functions. The obtained solutions include localized solitons, trigonometric solutions, pure cnoidal waves, and singular solutions in certain parameter range. Furthermore, it is observed that these solutions exist over a nonzero background.
Planar N=4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also extends to the planar space-time scattering amplitudes of the N=4 model, which show strong signs of Yangian invariance. However, in contradistinction to the spectral problem, this has not yet led to equations determining the exact amplitudes. We propose that the missing element is the spectral parameter, ubiquitous in integrable models. We show that it may indee…
We study BPS vortex configurations in three dimensional U(N) Yang-Mills theories with Chern-Simons interaction coupled to scalar fields carrying flavor. We consider two kind of configurations: local vortices (when the number of flavors $N_f=N$), and semi-local vortices (when $N_f>N$). In both cases we carefully analyze the electric and magnetic properties and present explicit numerical solutions.
We prove that three-dimensional $N=1$ supersymmetric Yang-Mills-Chern-Simons theory is finite to all loop orders. In general this leaves open the possibility that different regularization methods lead to different finite effective actions. We show that in this model dimensional regularization and regularization by dimensional reduction yield the same effective action. Consequently, the superfield approach preserves BRS invariance for this model.
We study quantum Chern-Simons theory as the large mass limit of the limit $D\to 3$ of dimensionally regularized topologically massive Yang-Mills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a higher-covariant derivative Yang-Mills term plus dimensional regularization. Working in the Landau gauge, we compute radiative corrections up to second order in perturbation theory and show that there is no two-loop correction to the one-loop shift $k\rightarrow k+ c_{\scriptscriptstyle V},\,\,k$ being the bare Chern-Simons pa…
We have constructed a four-fermion theory coupled to a Yang-Mills-Chern-Simons gauge field which admits static multi-vortex solutions. This is achieved through the introduction of an anomalous magnetic interation term in addition to the usual minimal coupling, and the appropriate choice of the fermion quartic coupling constant.
We apply novel techniques in planar superconformal Yang-Mills theory which stress the role of the Yangian algebra. We compute the first two Casimirs of the Yangian, which are identified with the first two local abelian Hamiltonians with periodic boundary conditions, and show that they annihilate the chiral primary states. We streamline the derivation of the R-matrix in a conventional spin model, and extend this computation to the gauge theory. We comment on higher-loop corrections and higher-loop integrability.
The two-point gauge correlation function in Yang--Mills--Chern--Simons theory in three dimensional Euclidean space is analysed by taking into account the non-perturbative effects of the Gribov horizon. In this way, we are able to describe the confinement and de-confinement regimes, which naturally depend on the topological mass and on the gauge coupling constant of the theory.
We present a Chern-Simons action for N=2 Super-Yang-Mills theory (SYM) in 'full' N=2 superspace (hyperspace) augmented by coordinates of the internal SU(2) group and show that this action can be reduced to the usual SYM action in the Harmonic hyperspace. We also discover that the 'choice' of Harmonic hyperspace is not unique and under suitable conditions, further reduction to the well-known Projective hyperspace is possible.
It has been argued by some authors that the parent action approach cannot be used in order to establish the duality between the 2+1 Abelian and non-Abelian Self-Dual (SD) and Yang-Mills-Chern-Simons (YMCS) models for all the coupling regimes. We propose here an alternative (perturbative) point of view, and show that this equivalence can be achieved with the parent action approach.
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfeld's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in q…
We construct a solution of eleven dimensional supergravity corresponding to a stack of M2 branes localized at the center of a particular eight dimensional hyper-Kaehler manifold constructed by Gauntlett, Gibbons, Papadopoulos, and Townsend, generalizing the earlier construction of Cherkis and Hashimoto. In the decoupling limit, this solution is dual to a Chern-Simons/Yang-Mills/Matter theory in 2+1 dimensions with N=3 supersymmetry, which flows in the infra red to a superconformal Chern-Simons/Matter system preserving N=6,8 supersymmetry, constructed recently by Aharony, Bergman, Jafferis, and…
We study one-loop correction to the Chern-Simons coefficient $κ=k/4π$ in $N=1,2,3$ supersymmetric Yang-Mills Chern-Simons systems. In the pure bosonic case, the shift of the parameter $k$ is known to be $k\rightarrow k + c_v$, where $c_v$ is the quadratic Casimir of the gauge group. In the $N=1$ case, the fermionic contribution cancels the bosonic contribution by half and the shift is $k \rightarrow k+ c_v/2$, making the theory anomalous if $c_v$ is odd. In the $N=2,3$ cases, the fermionic contribution cancels the bosonic contribution completely and there is no correction. We also calculate th…
We generalize the half-BPS Janus configuration of four-dimensional N=4 super Yang-Mills theory to allow the theta-angle, as well as the gauge coupling, to vary with position. We show that the existence of this generalization is closely related to the existence of novel three-dimensional Chern-Simons theories with N=4 supersymmetry. Another closely related problem, which we also elucidate, is the D3-NS5 system in the presence of a four-dimensional theta-angle.
We perform a detailed study of the Yangian symmetry of smooth supersymmetric Maldacena-Wilson loops in planar N=4 super Yang-Mills theory. This hidden symmetry extends the global superconformal symmetry present for these observables. A gauge-covariant action of the Yangian generators on the Wilson line is established that generalizes previous constructions built upon path variations. Employing these generators the Yangian symmetry is proven for general paths in non-chiral N=4 superspace at the first perturbative order. The bi-local piece of the level-one generators requires the use of a regula…
We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus in the limit when the torus becomes small. The zero-modes of the fields then decouple from the non-zero modes and give rise to a spectrum of states with energies that are given by multiples of the square of the coupling constant. We discuss the determination of this low-energy spectrum, both for simply connected gauge groups and for gauge groups of adjoint type, with a few examples worked out in detail.
We prove that three-dimensional N=1 supersymmetric Yang-Mills-Chern-Simons theory is finite to all loops. This leaves open the possibility that different regularization methods give different finite effective actions. We show that for this model dimensional regularization and regularization by dimensional reduction yield the same effective action.
We analyze the Chern-Simons-like term generation in the CPT-odd Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we study the anomalies of this model as well as its quantum stability. The whole analysis is performed within the algebraic renormalization theory, which is independent of the renormalization scheme. In addition, all results are valid to all orders in perturbation theory. We find that the Chern-Simons-like term is not generated by radiative corrections, just like its Abelian version. Additionally, the model is also free of gauge anomalies and quantum stable.
We study the large $N$ phase diagram of an asymptotically free UV completion of $\mathcal{N}=1$ $SU(N)$ super-Yang-Mills-Chern-Simons theory coupled to a single massive fundamental scalar multiplet with a quartic superpotential coupling. We compute the effective superpotential at small gauge coupling $λ\equiv N/k$, and combine this with previous results in the literature to obtain the full phase diagram in this regime. We find that tuning the UV parameters allows us to reach various phases and fixed points of Chern-Simons theory that were recently discovered using large $N$ techniques, as well…
In this work we study the behaviour of Yang--Mills--Chern--Simons theory coupled to a Higgs field in the fundamental representation by taking into account the effects of the presence of the Gribov horizon. By analyzing the infrared structure of the gauge field propagator, both confined and de-confined regions can be detected. The confined region corresponds to the appearance of complex poles in the propagators, while the de-confined one to the presence of real poles. One can move from one region to another by changing the parameters of the theory.
We propose that Baxter's Z-invariant six-vertex model at the rational gl(2) point on a planar but in general not rectangular lattice provides a way to study Yangian invariants. These are identified with eigenfunctions of certain monodromies of an auxiliary inhomogeneous spin chain. As a consequence they are special solutions to the eigenvalue problem of the associated transfer matrix. Excitingly, this allows to construct them using Bethe ansatz techniques. Conceptually, our construction generalizes to general (super) Lie algebras and general representations. Here we present the explicit form o…
By introducing an appropriate parent action and considering a perturbative approach, we establish, up to fourth order terms in the field and for the full range of the coupling constant, the equivalence between the noncommutative Yang-Mills-Chern-Simons theory and the noncommutative, non-Abelian Self-Dual model. In doing this, we consider two different approaches by using both the Moyal star-product and the Seiberg-Witten map.
A Hamiltonian analysis of Yang-Mills (YM) theory in (2+1) dimensions with a level $k$ Chern-Simons term is carried out using a gauge invariant matrix parametrization of the potentials. The gauge boson states are constructed and the contribution of the dynamical mass gap to the gauge boson mass is obtained. Long distance properties of vacuum expectation values are related to a Euclidean two-dimensional YM theory coupled to $k$ flavors of Dirac fermions in the fundamental representation. We also discuss the expectation value of the Wilson loop operator and give a comparison with previous results…
We construct the component action and supersymmetry transformations of the $\mathcal{N} = 3$ Chern-Simons-Yang-Mills theory that flows in the infra red to the $\mathcal{N} = 3$ super conformal quiver Chern-Simons gauge theory obtained by Jafferis and Tomasiello in \cite{Jafferis:2008qz}. We then obtain classical $\frac{1}{3}$-BPS (and anti-BPS) solutions all along the RG flow. The solutions display a rich structure, for example, there is a non-trivial moduli space. Various properties of supersymmetric monopole operators in the infra red super conformal field theory, such as global charges and …
