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 supermultiplets). 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.

We study supersymmetry breaking in theories with non-minimal multiplets (such as the complex linear or CNM multiplets), by using superspace higher derivative terms which give rise to new supersymmetry breaking vacuum solutions on top of the standard supersymmetric vacuum. We illustrate the decoupling of the additional massive sectors inside the complex linear and the CNM multiplets and show that only the Goldstino sector is left in the low energy limit. We also discuss the duality between non-minimal scalar multiplets and chiral multiplets in the presence of superspace higher derivatives. From the superspace Noether procedure we calculate the supercurrents, and we show that in the supersymmetry breaking vacuum the chiral superfield X which enters the Ferrara-Zumino supercurrent conservation equation does indeed flow in the IR to the chiral constrained Goldstino superfield. We also provide a description of the Goldstino sector in terms of the Samuel-Wess superfield for the supersymmetry breaking mechanism at hand.Comment: 31 pages. v4: discussion and references adde

We study (2, 2) and (4, 4) supersymmetric theories with superspace higher derivatives in two dimensions. A characteristic feature of these models is that they have several different vacua, some of which break supersymmetry. Depending on the vacuum, the equations of motion describe different propagating degrees of freedom. Various examples are presented which illustrate their generic properties. As a by-product we see that these new vacua give a dynamical way of generating non-linear realizations. In particular, our 2D (4, 4) example is the dimensional reduction of a 4D N = 2 model, and gives a new way for the spontaneous breaking of extended supersymmetry.

We present expressions for the supercurrents generated by a generic 4D, N = 1 theory of complex linear superfield Σ. We verify that these expressions satisfy the appropriate superspace conservation equations. Furthermore, we discuss the component projection in order to derive expressions for the energy-momentum tensor, the supersymmetry current and the R-symmetry current when available. In addition, we discuss aspects of the coupling of the theory to supergravity. Specifically, we present a straightforward method to select the appropriate formulations of supergravity that one must use in order to do the coupling. This procedure is controlled by a superfield X originating from the Super-Poincaré invariance of the theory. We apply these results to examples of theories with higher derivative terms.

We study partial supersymmetry breaking from N = 2 to N = 1 by adding non-linear terms to the N = 2 supersymmetry transformations. By exploiting the necessary existence of a deformed supersymmetry algebra for partial breaking to occur, we systematically use N = 2 projective superspace with central charges to provide a streamlined setup. For deformed O(2) and O(4) hypermultiplets, besides reproducing known results, we describe new models exhibiting partial supersymmetry breaking with and without higher-derivative interactions.