Emmanouil S. N. Raptakis

A bstract: Using the $$ \textrm{SO}\left(\mathcal{N}\right) $$ SO N superspace formulation for $$ \mathcal{N} $$ N -extended conformal supergravity in three dimensions, we derive all maximally supersymmetric backgrounds in the $$ \mathcal{N} $$ N = 4 case. The specific feature of this choice is that the so-called super Cotton tensor X ^IJKL = X ^{[ IJKL ]} , which exists for $$ \mathcal{N} $$ N ≥ 4, is equivalent to the scalar X defined by X ^IJKL = ε ^IJKL X . This scalar may be used as a deformation parameter. In the family of ( p , q ) anti-de Sitter (AdS) superspaces with p + q = 4, p ≥ q , it is known that X ≠ 0 exists only if p = 4 and q = 0. In general, the (4, 0) AdS superspaces are characterised by the structure group SL(2, ℝ ) × SO(4) and their geometry is determined by two constant parameters, S and X , of which the former determines the AdS curvature, while the R -symmetry curvature is determined by the parameters ( X + 2 S ) and ( X – 2 S ) in the left and right sectors of SU(2) _L × SU(2) _R , respectively. Setting S = 0 leads to the so-called deformed $$ \mathcal{N} $$ N = 4 Minkowski superspace $$ {\mathbbm{M}}_X^{\left.3\right|8} $$ M X 3 8 introduced thirteen years ago. We use projective-superspace techniques to construct general interacting supersymmetric field theories in $$ {\mathbbm{M}}_X^{\left.3\right|8} $$ M X 3 8 and demonstrate that they originate as massive deformations of the following two families of $$ \mathcal{N} $$ N = 4 theories in standard Minkowski superspace $$ {\mathbbm{M}}^{\left.3\right|8} $$ M 3 8 : (i) $$ \mathcal{N} $$ N = 4 superconformal field theories; and (ii) $$ \mathcal{N} $$ N = 4 supersymmetric gauge theories in $$ {\mathbbm{M}}^{\left.3\right|8} $$ M 3 8 which are not superconformal but possess the R -symmetry group SU(2) _L × SU(2) _R . Extensions of the theories in (ii) to $$ {\mathbbm{M}}_X^{\left.3\right|8} $$ M X 3 8 necessarily contain Chern-Simons terms at the component level. We also demonstrate the generation of topologically massive $$ \mathcal{N} $$ N = 4 supersymmetric gauge theories from radiative corrections in the hypermultiplet sector.

A bstract: Recently, new superparticle models have been proposed in the $$\mathcal{N}$$ -extended four and five-dimensional anti-de Sitter (AdS) superspaces, $${\text{AdS}}^{4|4\mathcal{N}}$$ and $${\text{AdS}}^{5|8\mathcal{N}}$$ , making use of a unique quadratic deformation to the AdS supersymmetric interval. In this paper we extend these considerations to the three and two-dimensional cases, and propose new two-derivative models for superparticles propagating in these AdS superspaces.

A bstract: We propose an $$ \mathcal{N} $$ N = 3 nonlinear multiplet coupled to conformal supergravity and use it to formulate the equations of motion for $$ \mathcal{N} $$ N = 3 Poincaré supergravity. These equations, which are naturally described in a new curved supergeometry with structure group SL(2 , ℂ), imply that the $$ \mathcal{N} $$ N = 3 super-Bach tensor vanishes, and thus every solution of Poincaré supergravity is a solution of conformal supergravity. The aforementioned superspace formulation, which we refer to as $$ \mathcal{N} $$ N = 3 Einstein superspace, is described in terms of two dimension-1 / 2 superfields: (i) the super-Weyl spinor W _α ; and (ii) a spinor isospinor $$ {\chi}_{\alpha}^i $$ χ α i .

In a supergravity framework, the $$ \mathcal{N} $$ N -extended anti-de Sitter (AdS) superspace in four spacetime dimensions, $$ {\textrm{AdS}}^{4\left|4\mathcal{N}\right.} $$ AdS 4 4 N , is a maximally symmetric background that is described by a curved superspace geometry with structure group SL(2, ℂ) × $$ \textrm{U}\left(\mathcal{N}\right) $$ U N . On the other hand, within the group-theoretic setting, $$ {\textrm{AdS}}^{4\left|4\mathcal{N}\right.} $$ AdS 4 4 N is realised as the coset superspace $$ \textrm{O}\textrm{Sp}\left(\left.\mathcal{N}\right|4;\mathbb{R}\right)/\left[\textrm{SL}\left(2,\mathbb{C}\right)\times \textrm{O}\left(\mathcal{N}\right)\right] $$ OSp N 4 ℝ / SL 2 ℂ × O N , with its structure group being SL(2, ℂ) × $$ \textrm{O}\left(\mathcal{N}\right) $$ O N . Here we explain how the two frameworks are related. We give two explicit realisations of $$ {\textrm{AdS}}^{4\left|4\mathcal{N}\right.} $$ AdS 4 4 N as a conformally flat superspace, thus extending the $$ \mathcal{N} $$ N = 1 and $$ \mathcal{N} $$ N = 2 results available in the literature. As applications, we describe: (i) a two-parameter deformation of the $$ {\textrm{AdS}}^{4\left|4\mathcal{N}\right.} $$ AdS 4 4 N interval and the corresponding superparticle model; (ii) some implications of conformal flatness for superconformal higher-spin multiplets and an effective action generating the $$ \mathcal{N} $$ N = 2 super-Weyl anomaly; and (iii) κ-symmetry of the massless AdS superparticle.

Three years ago, we proposed free off-shell models for $$ \mathcal{N} $$ N = 2 superconformal higher-spin multiplets in arbitrary conformally flat backgrounds, constructed conserved conformal higher-spin supercurrents for a massless hypermultiplet, and sketched the Noether procedure to generate its cubic couplings to the superconformal higher-spin multiplets. This paper is devoted to completing the Noether procedure. Specifically, we: (i) describe the unique off-shell primary extensions of the conformal higher-spin supercurrents; (ii) embed the off-shell superconformal prepotentials into primary unconstrained isotwistor multiplets; and (iii) present the unique gauge transformations of the hypermultiplet and the isotwistor prepotentials. An extension of the Noether procedure beyond the cubic level is also sketched, following the earlier $$ \mathcal{N} $$ N = 1 superconformal approach developed by the authors and Ponds in 2022. Our construction is based on making use of the polar hypermultiplet within the projective-superspace setting.

The Batalin-Vilkovisky formalism is applied to quantise the $$ \mathcal{N} $$ N = 1 supersymmetric generalisation of the Freedman-Townsend (FT) model, which was proposed by Lindström and Roček in 1983 in Minkowski superspace and is lifted to a supergravity background in this paper. This super FT theory describes a non-Abelian tensor multiplet and is known to be classically equivalent to a supersymmetric nonlinear sigma model. Using path integral considerations, we demonstrate that this equivalence holds at the quantum level in the sense that the quantum supercurrents in the two theories coincide. A modified Faddeev-Popov procedure is employed to quantise models for the $$ \mathcal{N} $$ N = 2 tensor multiplet in harmonic superspace. The obtained results agree with those derived by applying the Batalin-Vilkovisky scheme within the harmonic superspace setting.

We present higher-derivative deformations of the ModMax theory which preserve both U(1) duality symmetry and Weyl invariance. In particular, we single out a class of deformations expected to describe a low-energy effective action for the ModMax theory. We also elaborate on (higher-derivative) deformations of the $$ \mathcal{N} $$ N = 1 super ModMax theory.

We develop a superspace formulation for $$ \mathcal{N} $$ N = 3 conformal supergravity in four spacetime dimensions as a gauge theory of the superconformal group SU(2, 2|3). Upon imposing certain covariant constraints, the algebra of conformally covariant derivatives $$ {\nabla}_A=\left({\nabla}_a,{\nabla}_{\alpha}^i,{\nabla}_i^{\overset{\cdot }{\alpha }}\right) $$ ∇ A = ∇ a ∇ α i ∇ i α ⋅ is shown to be determined in terms of a single primary chiral spinor superfield, the super-Weyl spinor W _α of dimension +1/2 and its conjugate. Associated with W _α is its primary descendant B ⁱ _j of dimension +2, the super-Bach tensor, which determines the equation of motion for conformal supergravity. As an application of this construction, we present two different but equivalent action principles for $$ \mathcal{N} $$ N = 3 conformal supergravity. We describe the model for linearised $$ \mathcal{N} $$ N = 3 conformal supergravity in an arbitrary conformally flat background and demonstrate that it possesses U(1) duality invariance. Additionally, upon degauging certain local symmetries, our superspace geometry is shown to reduce to the U(3) superspace constructed by Howe more than four decades ago. Further degauging proves to lead to a new superspace formalism, called SU(3) superspace, which can also be used to describe $$ \mathcal{N} $$ N = 3 conformal supergravity. Our conformal superspace setting opens up the possibility to formulate the dynamics of the off-shell $$ \mathcal{N} $$ N = 3 super Yang-Mills theory coupled to conformal supergravity.