We find and classify the simplest ${\cal N}=2$ SUSY multiplets on AdS$_4$ which contain partially massless fields. We do this by studying representations of the ${\cal N}=2$, $d=3$ superconformal algebra of the boundary, including new shortening conditions that arise in the non-unitary regime. Unlike the ${\cal N}=1$ case, the simplest ${\cal N}=2$ multiplet containing a partially massless spin-2 is short, containing several exotic fields. More generally, we argue that ${\cal N}=2$ supersymmetry allows for short multiplets that contain partially massless spin-$s$ particles of depth $t=s-2$.
We construct unitary representations of (1,0) and (2,0) superconformal algebras in six dimensions by using superfields defined on harmonic superspaces with coset manifolds USp(2n)/[U(1)]^n, n=1,2. In the spirit of the AdS_7/CFT_6 correspondence massless conformal fields correspond to "supersingletons" in AdS_7. By tensoring them we produce all short representations corresponding to 1/2 and 1/4 BPS anti-de Sitter bulk states of which "massless bulk" representations are particular cases.
We find and classify the ${\cal N}=1$ SUSY multiplets on AdS$_4$ which contain partially massless fields. We do this by studying the non-unitary representations of the $d=3$ superconformal algebra of the boundary. The simplest super-multiplet which contains a partially massless spin-2 particle also contains a massless photon, a massless spin-$3/2$ particle and a massive spin-$3/2$ particle. The gauge parameters form a Wess-Zumino super-multiplet which contains the gauge parameters of the photon, the partially massless graviton, and the massless spin-$3/2$ particle. We find the AdS$_4$ action a…
An extended free fermionic construction of the internal N=1 world sheet supercurrent for four-dimensional superstring theory is given. We show how it can describe theories with massless fermions, and we discuss the corresponding N=2 superconformal algebra. As an intermediate step, we show that an internal N=2 global superconformal invariance occurs in any superstring theory with massless fermions at tree level. To demonstrate this fact, we give the N=2 supercurrents for a model with N=1 space-time supersymmetry and a model without space-time supersymmetry.
We determine the structure of geometrical superconformal anomalies for N=1 supersymmetric quantum field theories on curved superspace to all orders in h bar. For the massless Wess-Zumino model we show how these anomalies contribute to the local Callan-Symanzik equation which expresses the breakdown of superconformal symmetry in terms of the usual beta and gamma functions.
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is shown how various short representations can be obtained by parabolic induction. It is also shown that such short multiplets may admit several descriptions as superfields on different superspaces. In particular, this is the case for on-shell massless superfields. This allows a description of short representations as explicit products of fundamental fields. Superconformal transformations of analytic fields in real harmonic superspaces are given explicitly.
Celestial and momentum space amplitudes for massless particles are related to each other by a change of basis provided by the Mellin transform. Therefore properties of celestial amplitudes have counterparts in momentum space amplitudes and vice versa. In this paper, we study the celestial avatar of dual superconformal symmetry of $\mathcal{N}=4$ Yang-Mills theory. We also analyze various differential equations known to be satisfied by celestial $n$-point tree-level MHV amplitudes and identify their momentum space origins.
We study the minimal unitary representation (minrep) of SO(5,2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5,2) describes a massless conformal scalar field in five dimensions and admits a unique "deformation" which describes a massless conformal spinor. Scalar and spinor minreps of SO(5,2) are the 5d analogs of Dirac's singletons of SO(3,2). We then construct the minimal unitary representation of the unique 5d superconformal algebra F(4) with the even subalgebra SO(5,2) X SU(2). The minrep of F(4) describes…
In this paper we present a method of deforming to first order the stress-tensor and the supercurrent of the superstring corresponding to turning on NS-NS bosonic fields. Furthermore we discuss the difficulties associated with turning on spacetime fermions and R-R bosons. We also derive the gauge symmetries of the massless spacetime fields.
We propose a new off-shell formulation for the massless ${\cal N}=1$ supersymmetric multiplet of integer superspin $s$ in four dimensions, where $s =2,3,\dots$ (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-$s$ mu…
We show that there are two supersymmetric completions of the three-dimensional Chern-Simons theory of level k with gauge group U(N)xU(N) coupled to four sets of massless scalars and spinors in the bi-fundamental representation, if we require Sp(2) global symmetry with the matter fields in the fundamental representation of SU(4). One is the N=6 superconformal theory recently studied in arXiv:0806.1218 [hep-th] and another is a new theory with N=1 superconformal symmetry. We conjecture that the N=1 theory is dual to M theory on AdS_4 x Squashed S^7/Z_k.
Using the off-shell formulation for ${\cal N}=2$ conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved background and present their associated unconstrained gauge prepotentials. The latter are used to construct locally superconformal chiral actions, which are demonstrated to be gauge invariant in arbitrary conformally flat backgrounds. The main ${\cal N}=2$ results are then generalised to the ${\cal N}$-extended case. We also present the gauge-invariant field strengths for on-shell massless higher-spin ${\cal N}=2$ superm…
We perform a general analysis of representations of the superconformal algebras OSp(8/4,R) and OSp(8*/2N) in harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). In particular, all "short multiplets" are classified. Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant t…
We present the construction of exactly solvable superconformal field theories describing Type II string models compactified on compact G_2 manifolds. These models are defined by anti-holomorphic quotients of the form (CY*S^1)/Z_2, where we realize the Calabi-Yau as a Gepner model. In the superconformal field theory the Z_2 acts as charge conjugation implying that the representation theory of a W(2,4,6,8,10) algebra plays an important role in the construction of these models. Intriguingly, in all three examples we study, including the quintic, the massless spectrum in the Z_2 twisted sector of …
We carry out a general analysis of the representations of the superconformal algebras SU(2,2/N), OSp(8/4,R) and OSp(8^*/4) and give their realization in superspace. We present a construction of their UIR's by multiplication of the different types of massless superfields ("supersingletons"). Particular attention is paid to the so-called "short multiplets". Representations undergoing shortening have "protected dimension" and correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary confo…
We argue that Hitchin's equation determines not only the low energy effective theory but also describes the UV theory of four dimensional N=2 superconformal field theories when we compactify six dimensional $A_N$ $(0,2)$ theory on a punctured Riemann surface. We study the singular solution to Hitchin's equation and the Higgs field of solutions has a simple pole at the punctures; We show that the massless theory is associated with Higgs field whose residual is a nilpotent element; We identify the flavor symmetry associated with the puncture by studying the singularity of closure of the moduli s…
We study a class of classical solutions of three-dimensional N=6 superconformal Chern-Simons theory coupled with U(N) \times U(N) bi-fundamental matter fields. Especially, time evolutions of fuzzy spheres are discussed for both massless and massive cases. For the massive case, there are a variety of solutions having different behaviors according to the value of the mass. In addition to the time-dependent solutions, we analyze non-BPS static solutions which represent parallel M5/M5 or M5/anti-M5-branes suspended by multiple M2-branes. These solutions are similar to the fundamental strings conne…
We investigate the superconformal transformation properties of the supercurrent as well as of the superconformal anomalies themselves in d=4, N=1 supersymmetric quantum field theory. Matter supercurrent and anomalies are coupled to a classical background of minimal supergravity fields. On flat superspace, there exist two different types of the superconformal Ward identity (called S and B) which correspond to the flat space limits of old resp. new minimal background supergravity fields. In the present publication we give particular importance to the new minimal case. A general formalism is set …
We investigate the superconformal transformation properties of Green functions with one or more insertions of the supercurrent in N=1 supersymmetric quantum field theories. These Green functions are conveniently obtained by coupling the supercurrent and its trace to a classical supergravity background. We derive flat space superconformal Ward identities from diffeomorphisms and Weyl transformations on curved superspace. For the classification of potential quantum superconformal anomalies in the massless Wess-Zumino model on curved superspace a perturbative approach is pursued, using the BPHZ s…
Effective superpotentials for the phase with a confined photon are obtained in $N=1$ supersymmetric gauge theories. We use the results to derive the hyperelliptic curves which describe the Coulomb phase of $N=2$ theories with classical gauge groups, and thus extending the prior result for $SU(N_c)$ gauge theory by Elitzur et al. Moreover, adjusting the coupling constants in $N=1$ effective superpotentials to the values of $N=2$ non-trivial critical points we find new classes of $N=1$ superconformal field theories with an adjoint matter with a superpotential.
We present a general method for computing the central charges a and c of N=2 superconformal field theories corresponding to singular points in the moduli space of N=2 gauge theories. Our method relates a and c to the U(1)_R anomalies of the topologically twisted gauge theory. We evaluate these anomalies by studying the holomorphic dependence of the path integral measure on the moduli. We calculate a and c for superconformal points in a variety of gauge theories, including N=4 SU(N), N=2 pure SU(N) Yang-Mills, and USp(2N) with 1 massless antisymmetric and 4 massive fundamental hypermultiplets. …
We study the classification of 2-dimensional scale-invariant rigid special Kahler (RSK) geometries, which potentially describe the Coulomb branches of N=2 supersymmetric field theories in four dimensions. We show that this classification is equivalent to the solution of a set of polynomial equations by using an integrability condition for the central charge, scale invariance, constraints coming from demanding single-valuedness of physical quantities on the Coulomb branch, and properties of massless BPS states at singularities. We find solutions corresponding to lagrangian scale invariant theor…
We present a detailed study of the analytic structure, BPS spectra and superconformal points of the $ N=2 $ susy $ SU(2) $ gauge theories with $ N_f=1,2,3 $ massive quark hypermultiplets. We compute the curves of marginal stability with the help of the explicit solutions for the low energy effective actions in terms of standard elliptic functions. We show that only a few of these curves are relevant. As a generic example, the case of $ N_f=2 $ with two equal bare masses is studied in depth. We determine the precise existence domains for each BPS state, and show how they are compatible with the…
A self-consistent exposition of the theory of tree-level superamplitudes of the 4d N=4 and 6d N=(1,1) maximally supersymmetric Yang-Mills theories is provided. In 4d we work in non-chiral superspace and construct the superconformal and dual superconformal symmetry generators of the N=4 SYM theory using the non-chiral BCFW recursion to prove the latter. In 6d we provide a complete derivation of the standard and hidden symmetries of the tree-level superamplitudes of N=(1,1) SYM theory, again using the BCFW recursion to prove the dual conformal symmetry. Furthermore, we demonstrate that compact a…
We discuss the connection between Weyl$^2$ supergravity and superstrings and further discuss holography between 4-dimensional, ${\cal N}=4$ superconformal Weyl$^2$ supergravity and ${\cal N}=8$, higher spin-four theory on $AdS_5$. The Weyl$^2$ plus Einstein supergravity theory is a special kind of a bimetric gravity theory and consists of a massless graviton multiplet plus an additional massive spin-two supermultiplet. Here, we argue that the additional spin-two field and its superpartners originate from massive excitations in the open string sector; just like the ${\cal N}=4$ super Yang-Mills…
In the recent paper [1] the classification of non-unitary representations of the three dimensional superconformal group has been constructed. From AdS/CFT they must correspond to N=1 supermultiplets containing partially massless fields in $AdS_4$. Moreover, the simplest example of such supermultiplets which contains a partially massless spin-2 was explicitly constructed. In this paper we extend this result and develop explicit Lagrangian construction of general N=1 supermultiplets containing partially massless fields with arbitrary superspin. We use the frame-like gauge invariant description o…
We continue the classification of 2-dimensional scale-invariant rigid special Kahler (RSK) geometries. This classification was begun in [hep-th/0504070] where singularities corresponding to curves of the form y^2=x^6 with a fixed canonical basis of holomorphic one forms were analyzed. Here we perform the analysis for the y^2=x^5 type singularities. (The final maximal singularity type, y^2=x^3(x-1)^3, will be analyzed in a later paper.) These singularities potentially describe the Coulomb branches of N=2 supersymmetric field theories in four dimensions. We show that there are only 13 solutions …
We investigate representations of the conformal group that describe "massless" particles in the interior and at the boundary of anti-de Sitter space. It turns out that massless gauge excitations in anti-de Sitter are gauge "current" operators at the boundary. Conversely, massless excitations at the boundary are topological singletons in the interior. These representations lie at the threshold of two "unitary bounds" that apply to any conformally invariant field theory. Gravity and Yang-Mills gauge symmetry in anti-De Sitter is translated to global translational symmetry and continuous $R$-symm…
Based on the structure of the three-dimensional superconformal algebra we show that every irreducible ${\mathcal N}=6$ three-dimensional superconformal theory containes exactly one conserved U(1)-symmetry current in the stress tensor supermultiplet and that superconformal symmetry of every ${\mathcal N}=7$ superconformal theory is in fact enhanced to ${\mathcal N}=8$. Moreover, an irreducible ${\cal N}=8$ superconformal theory does not have any global symmetries. The first observation explains why all known examples of ${\mathcal N}=6$ superconformal theories have a global abelian symmetry.
Using a hybrid formalism, superstrings on AdS(3) x S(1) are studied in a manifestly supersymmetric manner. The world-sheet fields in this description including superspace coordinates are obtained through a field redefinition from the corresponding ones in the RNS formalism. The physical states are defined with the BRST cohomology as an N=4 topological string theory. The physical spectra for some lower mass levels are investigated. We identify two series of the space-time chiral primaries which have already been obtained from the analysis in the RNS formalism. We find that they are described by…
We develop techniques to calculate an index for four dimensional superconformal field theories. This superconformal index is counting BPS operators which preserve only one supercharge. To calculate the superconformal index we quantize the field theory on S^3 X R and show that the twisted theory has an appropriate mass gap. This allows for the interactions to be switched off continuously without the superconformal index being changed. We test those techniques for theories which go through a non-trivial RG flow and for Seiberg dual theories. This leads to the conjecture of some group/number theo…
Superconformal tensor calculus on an orbifold S^1/Z_2 is given in five-dimensional (5D) spacetime. The four-dimensional superconformal Weyl multiplet and various matter multiplets are induced on the boundary planes from the 5D supermultiplets in the bulk. We identify those induced 4D supermultiplets and clarify a general method for coupling the bulk fields to the matter fields on the boundaries in a superconformal invariant manner.
We consider the exact coupling constant dependence of extremal correlation functions of ${\cal N} = 2$ chiral primary operators in 4d ${\cal N} = 2$ superconformal gauge theories with gauge group SU(N) and N_f=2N massless fundamental hypermultiplets. The 2- and 3-point functions, viewed as functions of the exactly marginal coupling constant and theta angle, obey the tt* equations. In the case at hand, the tt* equations form a set of complicated non-linear coupled matrix equations. We point out that there is an ad hoc self-consistent ansatz that reduces this set of partial differential equation…
Within the framework of six-dimensional ${\cal N}=(1,0)$ conformal supergravity, we introduce new off-shell multiplets ${\cal O}{}^{*}(n)$, where $n=3,4,\dots,$ and use them to construct higher-rank extensions of the linear multiplet action. The ${\cal O}{}^{*}(n)$ multiplets may be viewed as being dual to well-known superconformal ${\cal O}(n)$ multiplets. We provide prepotential formulations for the ${\cal O}(n)$ and ${\cal O}{}^{*}(n)$ multiplets coupled to conformal supergravity. For every ${\cal O}{}^{*}(n)$ multiplet, we construct a higher derivative invariant which is superconformal on …
Aharony, Bergman, Jafferis and Maldacena have recently proposed a dual gravitational description for a family of superconformal Chern Simons theories in three spacetime dimensions. In this note we perform the one loop computation that determines the field theory superconformal index of this theory and compare with the index computed over the Fock space of dual supersymmetric gravitons. In the appropriate limit (large $N$ and large $k$) we find a perfect match.
We consider the entropy problem of AdS_3 black holes using the conformal field theory at the horizon. We observe that the supersymmetry is enhanced at the horizon of massless AdS_3 black hole. This allows us to determine the vacuum of the modular invariant conformal field theory to be the NS-ground state (which corresponds to AdS_3 spacetime). This is smoothly related to the R-ground state (corresponding to massless black hole) by a spectral flow, which can be understood as a superconformal transformation.
We report on the new approach to constructing superconformal extensions of the Calogero-type systems with an arbitrary number of involved particles. It is based upon the superfield gauging of non-abelian isometries of some supersymmetric matrix models. Among its applications, we focus on the new N=4 superconformal system yielding the U(2) spin Calogero model in the bosonic sector, and the one-particle case of this system, which is a new OSp(4|2) superconformal mechanics with non-dynamical U(2) spin variables. The characteristic feature of these models is that the strength of the conformal inve…
We show that four-dimensional N=2 supersymmetric SU(n) gauge theory for n>2 necessarily contains vacua with mutually non-local massless dyons, using only analyticity of the effective action and the weak coupling limit of the moduli space of vacua. A specific example is the Z_3 point in the exact solution for SU(3), and we study its effective Lagrangian. We propose that the low-energy theory at this point is an N=2 superconformal U(1) gauge theory containing both electrically and magnetically charged massless hypermultiplets.
This is the 8th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. The article reviews the superconformal index. It is often simpler to calculate than instanton partition functions, but nevertheless allows one to perform many nontrivial checks of conjectured dualities. It turns out to admit a representation in terms of a new type of topological field theory associated to the Riemann surfaces $C$ parameterising the class $\cal S$ theories.
The most general large ${\cal N}=4$ superconformal ${\cal W}_{\infty}$ algebra, containing in addition to the superconformal algebra one supermultiplet for each integer spin, is analysed in detail. It is found that the ${\cal W}_{\infty}$ algebra is uniquely determined by the levels of the two $\mathfrak{su}(2)$ algebras, a conclusion that holds both for the linear and the non-linear case. We also perform various cross-checks of our analysis, and exhibit two different types of truncations in some detail.
We analyze the constraints imposed by unitarity and crossing symmetry on the four-point function of the stress-tensor multiplet of ${\cal N}=8$ superconformal field theories in three dimensions. We first derive the superconformal blocks by analyzing the superconformal Ward identity. Our results imply that the OPE of the primary operator of the stress-tensor multiplet with itself must have parity symmetry. We then analyze the relations between the crossing equations, and we find that these equations are mostly redundant. We implement the independent crossing constraints numerically and find bou…
Recently N. Berkovits, motivated by the supertwistor description of ${\cal N}=4 D=4$ super Yang-Mills, considered the generalization of the ${\cal N}=1 D=4$ $θ$-twistor construction to D=10 and applied it for a compact covariant description of ${\cal N}=1 D=10$ super Yang-Mills. This supports the relevance of the $θ$-twistor as a supersymmetric twistor alternative to the well-known supertwistor. The minimal breaking of superconformal symmetry is an inherent property of the $θ$-twistor received from its fermionic components, described by a Grassmannian vector instead of a Grassmannian scalar in…
The symmetric orbifold of $\mathbb{T}^4$ is the CFT dual of string theory on AdS$_3\times {\rm S}^3 \times \mathbb{T}^4$ with minimal NS-NS flux. We study its symmetry algebra and provide evidence that it does not have any deformation parameter. This suggests that the symmetric orbifold is (at least locally) the most symmetrical CFT in its moduli space.
General 1-point toric blocks in all sectors of N=1 superconformal field theories are analyzed. The recurrence relations for blocks coefficients are derived by calculating their residues and large $Δ$ asymptotics.
We compute two-loop low-energy effective actions in Abelian Chern-Simons matter models with N=2 and N=3 supersymmetry up to four-derivative order. Calculations are performed with a slowly-varying gauge superfield background. Though the gauge superfield propagator depends on the gauge fixing parameter, it is shown that the obtained results are independent of this parameter. In the massless case the considered models are superconformal. We demonstrate that the superconformal symmetry strongly restricts the form of two-loop quantum corrections to the effective actions such that the obtained terms…
We study the quantum Seiberg-Witten periods of ${\cal N}=2$ superconformal field theories which are obtained by taking the scaling limit of ${\cal N}=2$ $SU(N_c)$ SQCD around the superconformal fixed point. The quantum Seiberg-Witten curves of these superconformal field theories are shown to be classified into the Schrödinger type and the SQCD type, which depend on flavor symmetry at the fixed point. We study the quantum periods and compute the differential operators which relate the quantum periods to the classical ones up to the fourth-order in the deformation parameter.
We provide the geometrical meaning of the ${\cal N}=4$ superconformal index. With this interpretation, the ${\cal N}=4$ superconformal index can be realized as the partition function on a Scherk-Schwarz deformed background. We apply the localization method in TQFT to compute the deformed partition function since the deformed action can be written as a $δ_ε$-exact form. The critical points of the deformed action turn out to be the space of flat connections which are, in fact, zero modes of the gauge field. The one-loop evaluation over the space of flat connections reduces to the matrix integral…
Dual conformal symmetry and Yangian symmetry are symmetries of amplitudes that have aided the study of scattering amplitudes in highly supersymmetric theories like ${\cal N}=4$ SYM and ABJM. However, in general such symmetries are absent from the theories with lesser or no supersymmetry. In this paper, we show that the tree level $2\to 2$ scattering amplitude in the 3d ${\cal N}=2$ Chern-Simons theory coupled to a fundamental chiral multiplet is dual superconformal invariant. In the 't Hooft large $N$ limit, the $2\to 2$ scattering amplitude in this theory has been shown to be tree-level exact…
We present a comprehensive analysis of supersymmetry anomalies in the free and massless Wess-Zumino (WZ) model in perturbation theory. At the classical level the model possesses ${\mathcal N}=1$ superconformal symmetry, which is partially broken by quantum anomalies. The form of the anomalies and the part of the symmetry they break depend on the multiplet of conserved currents used. It was previously shown that the R-symmetry anomaly of the conformal current multiplet induces an anomaly in Q-supersymmetry, which appears first in 4-point functions. Here we confirm this result by an explicit 1-l…
Building on the five-dimensional constructions in hep-th/0601177, we provide a unified description of four-dimensional N = 2 superconformal off-shell multiplets in projective superspace, including a realization in terms of N = 1 superfields. In particular, superconformal polar multiplets are consistently defined for the first time. We present new 4D N = 2 superconformal sigma-models described by polar multiplets. Such sigma-models realize general superconformal couplings in projective superspace, but involve an infinite tale of auxiliary N = 1 superfields. The auxiliaries should be eliminated …
We study the entropy associated with the Janus interface in a 4$d$ $\mathcal{N}=2$ superconformal field theory. With the entropy defined as the interface contribution to an entanglement entropy we show, under mild assumptions, that the Janus interface entropy is proportional to the geometric quantity called Calabi's diastasis on the space of $\mathcal{N}=2$ marginal couplings, confirming an earlier conjecture by two of the authors and generalizing a similar result in two dimensions. Our method is based on a CFT consideration that makes use of the Casini-Huerta-Myers conformal map from the flat…
In spacetime dimension two, pure Yang-Mills possesses no physical degrees of freedom, and consequently it admits a supersymmetric extension to couple to an arbitrary number, N say, of Majorana-Weyl gauginos. This results in (N,0) super Yang-Mills. Further, its dimensional reduction to mechanics doubles the number of supersymmetries, from N to N+N, to include conformal supercharges, and leads to a superconformal Yang-Mills quantum mechanics with symmetry group OSp(N|2,R). We comment on its connection to AdS_2 \times S^{N-1} and reduction to a supersymmetric Calogero model.
In this note we calculate the fusion coefficients for minimal series representations of the N=2 superconformal algebra by using a modified Verlinde's formula, and obtain associative and commutative fusion algebras with non-negative integral fusion coefficients at each level. Some references are added.
We study which bulk couplings contribute to the $S^3$ free energy $F(\mathfrak{m})$ of three-dimensional ${\cal N} = 2$ superconformal field theories with holographic duals, potentially deformed by boundary real-mass parameters $\mathfrak{m}$. In particular, we show that $F(\mathfrak{m})$ is independent of a large class of bulk couplings that include non-chiral F-terms and all D-terms. On the other hand, in general, $F(\mathfrak{m})$ does depend non-trivially on bulk chiral F-terms, such as prepotential interactions, and on bulk real-mass terms. These conclusions can be reached solely from pro…
I review the approach [1] to the one-loop low-energy effective action in the hypermultiplet sector for N=2 superconformal models. Any such a model contains an N=2 vector multiplet and some number of hypermultiplets. We found a general expression for the low-energy effective action in the form of a proper-time integral. The leading space-time dependent contributions to the effective action are derived and their bosonic component structure is analyzed. The component action contains terms with three and four space-time derivatives of component fields and has the Chern-Simons-like form.
By coupling {\cal N}=8 superconformal matter to {\cal N}=8 superconformal Chern-Simons gravity in three dimensions we obtain theories with novel terms in the scalar potential leading to AdS_3 solutions and superconformal symmetry breaking. If we start from the theory derived by Bagger, Lambert and Gustavsson, our coupled theory either inherits the SO(4) gauge group or reduces it to SO(3). If the construction is instead based on a free matter theory we find that the gravitational topological gauging also requires the introduction of a Chern-Simons gauge sector resulting in a consistent theory f…
Within the supertwistor approach, we analyse the superconformal structure of 4D N = 2 compactified harmonic/projective superspace. In the case of 5D superconformal symmetry, we derive the superconformal Killing vectors and related building blocks which emerge in the transformation laws of primary superfields. Various off-shell superconformal multiplets are presented both in 5D harmonic and projective superspaces, including the so-called tropical (vector) multiplet and polar (hyper)multiplet. Families of superconformal actions are described both in the 5D harmonic and projective superspace sett…
We find a general formula for the operator mixing on the $\mathbb{S}^4$ of chiral primary operators (CPO) for the ${\cal N}=4$ theory at large $N$ in terms of Chebyshev polynomials. As an application, we compute the correlator of a CPO and a Wilson loop, reproducing an earlier result by Giombi and Pestun obtained from a two-matrix model proposal. Finally, we discuss a simple method to obtain correlators in general ${\cal N}=2$ superconformal field theories in perturbation theory in terms of correlators of the ${\cal N}=4$ theory.
