Tensor Superfields Research Articles

Symmetries of supergravity backgrounds and supersymmetric field theory

In four spacetime dimensions, all mathcal{N} = 1 supergravity-matter systems can be formulated in the so-called U(1) superspace proposed by Howe in 1981. This paper is devoted to the study of those geometric structures which characterise a background U(1) superspace and are important in the context of supersymmetric field theory in curved space. We introduce (conformal) Killing tensor superfields {mathrm{ell}}_{left({alpha}_1dots {alpha}_mright)left({overset{cdot }{alpha}}_1dots {overset{cdot }{alpha}}_nright)} , with m and n non-negative integers, m + n > 0, and elaborate on their significance in the following cases: (i) m = n = 1; (ii) m − 1 = n = 0; and (iii) m = n > 1. The (conformal) Killing vector superfields {mathrm{ell}}_{alpha overset{cdot }{alpha }} generate the (conformal) isometries of curved superspace, which are symmetries of every (conformal) supersymmetric field theory. The (conformal) Killing spinor superfields ℓα generate extended (conformal) supersymmetry transformations. The (conformal) Killing tensor superfields with m = n > 1 prove to generate all higher symmetries of the (massless) massive Wess-Zumino operator.

Conformally compactified Minkowski superspaces revisited

Starting from the standard supertwistor realizations for conformally compactified N-extended Minkowski superspaces in three and four space-time dimensions, we elaborate on alternative realizations in terms of graded two-forms on the dual supertwistor spaces. The construction is further generalized to the cases of 4D N=2 and 3D N-extended harmonic/projective superspaces. We present a superconformal Fourier expansion of tensor superfields on the 4D N=2 harmonic/projective superspace.

Vafa-Witten theory onN= 2 andN= 4 twisted superspace in four dimensions

We construct a new off-shell twisted hypermultiplet with a scalar and an anti-self-dual tensor superfields. Using the N=2 twisted superspace formalism, we construct a Donaldson-Witten theory coupled to the hypermultiplet. We show that this action possesses the Vafa-Witten type N=4 twisted supersymmetry at the on-shell level. We also reconstruct the action using a N=4 twisted superconnection formalism.

A note on composite operators in N=4 SYM

We discuss composite operators in N=4 super Yang-Mills theory and their realisations as superfields on different superspaces. The superfields that realise various operators on analytic superspace may be different in the free, interacting and quantum theories. In particular, in the quantum theory, there is a restricted class of operators that can be written as analytic tensor superfields. This class includes all series B and C operators in the theory as well as some series A operators which saturate the unitarity bounds. Operators of this type are expected to be protected from renormalisation.

Tensor analysis on conformal supergeometry and the ghost action of the superstring

The orthogonal decomposition technique is extended to the physical and ghost tensor superfields on the two-dimensional conformal supergeometry. This method makes the meaning of the superfield functional integral clearer. The form of the ghost action of the superstring in the superspace formulation is discussed on this basis.