Supercurrent Multiplet Research Articles

Embedding formalism for (p, q) AdS superspaces in three dimensions

We develop an embedding formalism for (p, q) anti-de Sitter (AdS) superspaces in three dimensions by using a modified version of their supertwistor description given in the literature. A coset construction for these superspaces is worked out. We put forward a program of constructing a supersymmetric analogue of the Bañados metric, which is expected to be a deformation of the (p, q) AdS superspace geometry by a two-dimensional conformal (p, q) supercurrent multiplet.

On higher-spin mathcal{N} = 2 supercurrent multiplets

We elaborate on the structure of higher-spin mathcal{N} = 2 supercurrent multiplets in four dimensions. It is shown that associated with every conformal supercurrent {J}_{alpha (m)overset{cdot }{alpha }(n)} (with m, n non-negative integers) is a descendant {J}_{alpha left(m+1right)overset{cdot }{alpha}left(n+1right)}^{ij} with the following properties: (a) it is a linear multiplet with respect to its SU(2) indices, that is {D}_{beta}^{Big(i}{J}_{alpha left(m+1right)overset{cdot }{alpha}left(n+1right)}^{jkBig)}=0 and {overline{D}}_{dot{beta}}^{Big(i}{J}_{alpha left(m+1right)overset{cdot }{alpha}left(n+1right)}^{jkBig)}=0 ; and (b) it is conserved, {partial}^{beta overset{cdot }{beta }}{J}_{beta alpha (m)overset{cdot }{beta}overset{cdot }{alpha }(n)}^{ij}=0 . Realisations of the conformal supercurrents {J}_{alpha (s)overset{cdot }{alpha }(s)} , with s = 0, 1, …, are naturally provided by a massless hypermultiplet and a vector multiplet. It turns out that such supercurrents and their linear descendants {J}_{alpha left(s+1right)overset{cdot }{alpha}left(s+1right)}^{ij} do not occur in the harmonic-superspace framework recently described by Buchbinder, Ivanov and Zaigraev. Making use of a massive hypermultiplet, we derive non-conformal higher-spin mathcal{N} = 2 supercurrent multiplets. Additionally, we derive the higher symmetries of the kinetic operators for both a massive and massless hypermultiplet. Building on this analysis, we sketch the construction of higher-derivative gauge transformations for the off-shell arctic multiplet Υ(1), which are expected to be vital in the framework of consistent interactions between Υ(1) and superconformal higher-spin gauge multiplets.

Three‐Point Functions of Higher‐Spin Supercurrents in 4D N=1${{\cal N}}=1$ Superconformal Field Theory

AbstractWe develop a general formalism to study the three‐point correlation functions of conserved higher‐spin supercurrent multiplets in 4D superconformal theory. All the constraints imposed by superconformal symmetry on the three‐point function are systematically derived for arbitrary , thus reducing the problem mostly to computational and combinatorial. As an illustrative example, we explicitly work out the allowed tensor structures contained in , where is the supercurrent. We find that this three‐point function depends on two independent tensor structures, though the precise form of the correlator depends on whether r is even or odd. The case reproduces the three‐point function of the ordinary supercurrent derived by Osborn. Additionally, we present the most general structure of mixed correlators of the form and , where L is the flavour current multiplet.

Progress on cubic interactions of arbitrary superspin supermultiplets via gauge invariant supercurrents

We consider cubic interactions of the form s−Y−Y between a massless integer superspin s supermultiplet and two massless arbitrary integers or half integer superspin Y supermultiplets. We focus on non-minimal interactions generated by gauge invariant supercurrent multiplets which are bilinear in the superfield strength of the superspin Y supermultiplet. We find two types of consistent supercurrents. The first one corresponds to conformal integer superspin s supermultiplets, exist only for even values of s,s=2ℓ+2, for arbitrary values of Y and it is unique. The second one, corresponds to Poincaré integer superspin s supermultiplets, exist for arbitrary values of s and Y.

Field theories with (2,0) AdS supersymmetry in N=1 AdS superspace

In three dimensions, it is known that field theories possessing extended $(p,q)$ anti-de Sitter (AdS) supersymmetry with ${\cal N}=p+q \geq 3$ can be realised in (2,0) AdS superspace. Here we present a formalism to reduce every field theory with (2,0) AdS supersymmetry to ${\cal N}=1$ AdS superspace. As nontrivial examples, we consider supersymmetric nonlinear sigma models formulated in terms of ${\cal N}=2$ chiral and linear supermultiplets. The $(2,0) \to (1,0)$ AdS reduction technique is then applied to the off-shell massless higher-spin supermultiplets in (2,0) AdS superspace constructed in [1]. As a result, for each superspin value $\hat s$, integer $(\hat s= s)$ or half-integer $(\hat s= s+1/2)$, with $s=1,2,\dots $, we obtain two off-shell formulations for a massless ${\cal N}=1$ superspin-$\hat s$ multiplet in AdS${}_3$. These models prove to be related to each other by a superfield Legendre transformation in the flat superspace limit, but the duality is not lifted to the AdS case. Two out of the four series of ${\cal N}=1$ supersymmetric higher-spin models thus derived are new. The constructed massless ${\cal N}=1$ supersymmetric higher-spin actions in AdS${}_3$ are used to formulate (i) higher-spin supercurrent multiplets in ${\cal N}=1$ AdS superspace; and (ii) new topologically massive higher-spin off-shell supermultiplets. Examples of ${\cal N}=1$ higher-spin supercurrents are given for models of a complex scalar supermultiplet. We also present two new off-shell formulations for a massive ${\cal N}=1$ gravitino supermultiplet in AdS${}_3$.

Boundaries and supercurrent multiplets in 3D Landau-Ginzburg models

Theories with 3D mathcal{N} = 2 bulk supersymmetry may preserve a 2D mathcal{N} = left(0, 2right) subalgebra when a boundary is introduced, possibly with localized degrees of freedom. We propose generalized supercurrent multiplets with bulk and boundary parts adapted to such setups. Using their structure, we comment on implications for the {overline{Q}}_{+} -cohomology. As an example, we apply the developed framework to Landau-Ginzburg models. In these models, we study the role of boundary degrees of freedom and matrix factorizations. We verify our results using quantization.

On Toverline{T} deformations and supersymmetry

We investigate the “ Toverline{T} ” deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the Toverline{T} deforming operator can be constructed as a super-symmetric descendant. Here we focus on mathcal{N} = left(1,0right) and mathcal{N} = left(1,1right) supersymmetry. As an example, we analyse in detail the Toverline{T} deformation of a free mathcal{N} = left(1,0right) supersymmetric action. We also argue that the link between Toverline{T} and string theory can be extended to su-perstrings: by analysing the light-cone gauge fixing for superstrings in flat space, we show the correspondence of the string action to the Toverline{T} deformation of a free theory of eight mathcal{N} = left(1,1right) scalar multiplets on the nose. We comment on how these constructions relate to the geometrical interpretations of Toverline{T} deformations that have recently been discussed in the literature.

On TT¯ deformations and supersymmetry

We investigate the “TT¯ ” deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the TT¯ deforming operator can be constructed as a super-symmetric descendant. Here we focus on N=(10) and N=(11) supersymmetry. As an example, we analyse in detail the TT¯ deformation of a free N=(10) supersymmetric action. We also argue that the link between TT¯ and string theory can be extended to su-perstrings: by analysing the light-cone gauge fixing for superstrings in flat space, we show the correspondence of the string action to the TT¯ deformation of a free theory of eight N=(11) scalar multiplets on the nose. We comment on how these constructions relate to the geometrical interpretations of TT¯ deformations that have recently been discussed in the literature.

Integer superspin supercurrents of matter supermultiplets

In recent papers [18, 21] we demonstrated that consistent and non-trivial linear transformations of matter supermultiplets generate half-integer superspin supercurrents and the cubic interactions between matter and half-integer superspin supermultiplets. In this work we show that consistent and non-trivial antilinear transformations of matter superfields lead to the construction of integer superspin supercurrents and the cubic interactions between mater and integer superspin supermultiplets. Applying Noether’s method to these transformations, we find new integer superspin supercurrents for the case of a free massless chiral superfield. Furthermore, we use them to find new integer superspin supercurrent multiplets for a massive chiral superfield and a chiral superfield with a linear superpotential. Also various selection rules for such interactions are found.

N=2 supersymmetric higher spin gauge theories and current multiplets in three dimensions

We describe several families of primary linear supermultiplets coupled to three-dimensional ${\cal N}=2$ conformal supergravity and use them to construct topological $BF$-type terms. We introduce conformal higher-spin gauge superfields and associate with them Chern-Simons-type actions that are constructed as an extension of the linearised action for ${\cal N}=2$ conformal supergravity. These actions possess gauge and super-Weyl invariance in any conformally flat superspace and involve a higher-spin generalisation of the linearised ${\cal N}=2$ super-Cotton tensor. For massless higher-spin supermultiplets in (1,1) anti-de Sitter (AdS) superspace, we propose two off-shell Lagrangian gauge formulations, which are related to each other by a dually transformation. Making use of these massless theories allows us to formulate consistent higher-spin supercurrent multiplets in (1,1) AdS superspace. Explicit examples of such supercurrent multiplets are provided for models of massive chiral supermultiplets. Off-shell formulations for massive higher-spin supermultiplets in (1,1) AdS superspace are proposed.

Higher spin supercurrents in anti-de Sitter space

We propose higher spin supercurrent multiplets for mathcal{N}=1 supersymmetric field theories in four-dimensional anti-de Sitter space (AdS). Their explicit realisations are derived for various supersymmetric theories, including a model of N massive chiral scalar superfields with an arbitrary mass matrix. We also present new off-shell gauge formulations for the massless mathcal{N}=1 supersymmetric multiplet of integer superspin s in AdS, where s = 2, 3, . . . , as well as for the massless gravitino multiplet (superspin s = 1) which requires special consideration.

24+24 real scalar multiplet in four dimensional N=2 conformal supergravity

Starting from the 48+48 component multiplet of supercurrents for a rigid N=2 tensor multiplet in four spacetime dimensions, we obtain the transformation of the linearized supergravity multiplet which couples to this supercurrent multiplet. At the linearized level, this 48+48 component supergravity multiplet decouples into the 24+24 component linearized standard Weyl multiplet and a 24+24 component irreducible matter multiplet containing a real scalar field. By a consistent application of the supersymmetry algebra with field dependent structure constants appropriate to N=2 conformal supergravity, we find the full transformation law for this multiplet in a conformal supergravity background. By performing a field redefinition and switching off the conformal supergravity background, the multiplet is equivalent to the one introduced by Howe et al in flat space as a constrained real scalar superfield. We present a set of constraints which can be consistently imposed on this multiplet to obtain a restricted minimal 8+8 off-shell matter multiplet. We also show as an example the precise embedding of the tensor multiplet inside this multiplet.

Higher spin superfield interactions with complex linear supermultiplet: conserved supercurrents and cubic vertices

We continue the program of constructing cubic interactions between matter and higher spin supermultiplets. In this work we consider a complex linear superfield and we find that it can have cubic interactions only with supermultiplets with propagating spins j = s + 1, j = s + 1/2 for any non-negative integer s (half-integer superspin super-multiplets). We construct the higher spin supercurrent and supertrace, these compose the canonical supercurrent multiplet which generates the cubic interactions. We also prove that for every s there exist an alternative minimal supercurrent multiplet, with vanishing supertrace. Furthermore, we perform a duality transformation in order to make contact with the corresponding chiral theory. An interesting result is that the dual chiral theory has the same coupling constant with the complex linear theory only for odd values of s, whereas for even values of s the coupling constants for the two theories have opposite signs. Additionally we explore the component structure of the supercurrent multiplet and derive the higher spin currents. We find two bosonic currents for spins j = s and j = s + 1 and one fermionic current for spin j = s + 1/2.

Chiral algebras in Landau-Ginzburg models

Chiral algebras in the cohomology of the {overline{Q}}_{+} supercharge of two-dimensional mathcal{N}=left(0,2right) theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For mathcal{N}=left(0,2right) Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the mathcal{N}=left(2,2right) models and consider some examples.

The massless integer superspin multiplets revisited

We propose a new off-shell formulation for the massless mathcal{N} = 1 supersymmetric multiplet of integer superspin s in four dimensions, where s = 2, 3, . . . (the s = 1 case corresponds to the gravitino multiplet). Its gauge freedom matches that of the superconformal superspin-s multiplet described in arXiv:1701.00682. The gauge-invariant action involves two compensating multiplets in addition to the superconformal superspin-s multiplet. Upon imposing a partial gauge fixing, this action reduces to the one describing the so-called longitudinal formulation for the massless superspin-s multiplet. Our new model is shown to possess a dual realisation obtained by applying a superfield Legendre transformation. We present a non-conformal higher spin supercurrent multiplet associated with the new integer superspin theory. This fermionic supercurrent is shown to occur in the Fayet-Sohnius model for a massive mathcal{N} = 2 hypermultiplet. We also give a new off-shell realisation for the massless gravitino multiplet.

Non-conformal higher spin supercurrents

In four spacetime dimensions there exist two off-shell formulations for the massless multiplet of superspin (s+12), where s=2,3,…. These supersymmetric higher spin gauge theories, known as longitudinal and transverse, are dual to each other and describe two massless fields of spin (s+12) and (s+1) upon elimination of the auxiliary fields. They respectively reduce, in the limiting case of s=1, to the linearised actions for the old minimal and the n=−1 non-minimal N=1 supergravity theories. Associated with these gauge massless theories are non-conformal higher spin supercurrent multiplets which we describe. We demonstrate that the longitudinal higher spin supercurrents are realised in the model for a massive chiral scalar superfield only if s is odd, s=2n+1, with n=1,2,….

Higher Spin Superfield Interactions with the Chiral Supermultiplet: Conserved Supercurrents and Cubic Vertices

We investigate cubic interactions between a chiral superfield and higher spin superfields corresponding to irreducible representations of the 4 D , N = 1 super-Poincaré algebra. We do this by demanding an invariance under the most general transformation, linear in the chiral superfield. Following Noether’s method we construct an infinite tower of higher spin supercurrent multiplets which are quadratic in the chiral superfield and include higher derivatives. The results are that a single, massless, chiral superfield can couple only to the half-integer spin supermultiplets ( s + 1 , s + 1 / 2 ) and for every value of spin there is an appropriate improvement term that reduces the supercurrent multiplet to a minimal multiplet which matches that of superconformal higher spins. On the other hand a single, massive, chiral superfield can couple only to higher spin supermultiplets of type ( 2 l + 2 , 2 l + 3 / 2 ) (only odd values of s, s = 2 l + 1 ) and there is no minimal multiplet. Furthermore, for the massless case we discuss the component level higher spin currents and provide explicit expressions for the integer and half-integer spin conserved currents together with a R-symmetry current.

Implications of N $$ \mathcal{N} $$ = 5, 6 superconformal symmetry in three spacetime dimensions

For general N=5 and N=6 superconformal field theories in three dimensions, we compute the three-point correlation functions of the supercurrent multiplets. In each case, N=5 and N=6, the functional form of this correlator is uniquely fixed modulo an overall coefficient which is related, by superconformal Ward identities, to the parameter in the two-point function of the supercurrent. The structure of the correlation functions obtained is consistent with the property that every N=5 superconformal field theory, considered as a special N=4 theory, is invariant under the mirror map.

Supercurrent multiplet correlators at weak and strong coupling

Correlators of gauge invariant operators provide useful information on the dynamics, phases and spectra of a quantum field theory. In this paper, we consider N=1 supersymmetric theories and focus our attention on the supercurrent multiplet. We give a complete characterization of two-point functions of operators belonging to such multiplet, like the energy-momentum tensor and the supercurrent, and study the relations between them. We discuss instances of weakly coupled and strongly coupled theories, in which different symmetries, like conformal invariance and supersymmetry, may be conserved and/or spontaneously or explicitly broken. For theories at strong coupling, we exploit AdS/CFT techniques. We provide a holographic description of different properties of a strongly coupled theory, including a realization of the Goldstino mode in a simple illustrative model.

Simplifying instanton corrections to $ \mathcal{N} $ = 4 SYM correlators

We compute instanton corrections to non-minimal correlation functions of chiral primary operators in the N=4 super Yang-Mills super-current multiplet. Using a representation in terms of Mellin integrals, we find that these corrections can be written as conformal integrals in AdS_5 times certain "kinematic" prefactors that are independent of the instanton moduli. We then consider the consecutive, pairwise light-like limit x_{i, i+1}^2 -> 0 of such correlators, and prove that the ratio between the instanton contribution and the corresponding tree-level expression vanishes in this limit. We also speculate on the extension to the non-perturbative level of the proposed duality with polygonal Wilson loops and briefly discuss its potential implications for scattering amplitudes.