Related papers: Projective multiplets and hyperkahler cones in con…
We provide a unified description of the three covariant superspace approaches to ${\cal N}=2$ conformal supergravity in four dimensions: (i) conformal superspace; (ii) $\mathsf{U}(2)$ superspace; and (iii) $\mathsf{SU}(2)$ superspace. Each…
We develop a new off-shell formulation for five-dimensional (5D) conformal supergravity obtained by gauging the 5D superconformal algebra in superspace. An important property of the conformal superspace introduced is that it reduces to the…
Basics of ${\cal N}=2, 4D$ conformal and Einstein supergravities in the harmonic superspace approach are outlined. The crucial merit of this formulation consists in that the relevant off-shell supermultiplets, in particular ${\cal N}=2, 4D$…
We construct manifestly $4D, \mathcal{N}=2$ supersymmetric and gauge invariant off-shell cubic couplings of matter hypermultiplets to the higher integer spin gauge $\mathcal{N}=2$ multiplets introduced in arXiv:2109.07639 [hep-th]. The…
This paper describes a fully covariant approach to harmonic superspace. It is based on the conformal superspace description of conformal supergravity and involves extending the supermanifold M^{4|8} by the tangent bundle of CP^1. The…
We construct N=2 supersymmetric nonlinear sigma models on the cotangent bundles over the non-compact exceptional Hermitian symmetric spaces M=E_{6(-14)}/SO(10)xU(1) and E_{7(-25)}/E_6xU(1). In order to construct them we use the projective…
We propose a superfield method to construct off-shell actions for N-extended conformal supergravity theories in three space-time dimensions. It makes use of the superform technique to engineer supersymmetric invariants. The method is…
We construct off-shell superconformal actions of hypermultiplets coupled with non-Abelian gauge multiplets in three-dimensional N = 3 and N = 4 projective superspaces. We establish the explicit embeddings of the N = 2 vector and adjoint…
Using projective superspace techniques, we consider 4D N = 2 and 5D N = 1 gauged supersymmetric nonlinear sigma-models for which the hyper-Kahler target space is (an open domain of the zero section of) the cotangent bundle of a…
We develop a formalism to construct supersymmetric backgrounds within the superspace formulation for five-dimensional (5D) conformal supergravity given in arXiv:0802.3953. Our approach is applicable to any off-shell formulation for 5D…
We analyse the relationship between the N=2 harmonic and projective superspaces which are the only approaches developed to describe general N=2 super Yang-Mills theories in terms of off-shell supermultiplets with conventional supersymmetry.…
We develop geometric superspace settings to construct arbitrary higher derivative couplings (including R^n terms) in three-dimensional supergravity theories with N=1,2,3 by realising them as conformal supergravity coupled to certain…
We describe the projective superspace approach to supersymmetric models with off-shell $(0,4)$ supersymmetry in two dimensions. In addition to the usual superspace coordinates, projective superspace has extra bosonic variables -- one…
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…
This is a light and short review on the geometry of hypermultiplets coupled to supergravity and its appearance in string theory. As is long known, the target space of the hypermultiplet sigma-model is a quaternion-K\"ahler (QK) manifold of…
We address the construction of four-dimensional N=2 supersymmetric nonlinear sigma models on tangent bundles of arbitrary Hermitian symmetric spaces starting from projective superspace. Using a systematic way of solving the (infinite number…
We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special}…
We construct the hyperkahler cones corresponding to the Quaternion-Kahler orthogonal Wolf spaces SO(n+4)/(SO(n)xSO(4)) and their non-compact versions, which appear in hypermultiplet couplings to N=2 supergravity. The geometry is completely…
We computed the actions for the 1D N=5 sigma-models with respect to the two inequivalent (2,8,6) multiplets. 4 supersymmetry generators are manifest, while the constraint originated by imposing the 5-th supersymmetry automatically induces a…
The off-shell actions for $\cal N$-extended conformal supergravity theories in three dimensions were formulated in [1,2] for $1\leq {\cal N} \leq 6$ using a universal approach. Each action is generated by a closed super three-form which is…