Variant supercurrents and Noether procedure

Abstract

Consistent supercurrent multiplets are naturally associated with linearized off-shell supergravity models. In S.M. Kuzenko, J. High Energy Phys. 1004, 022 (2010 we presented the hierarchy of such supercurrents which correspond to all the models for linearized 4D N = 1 supergravity classified a few years ago. Here we analyze the correspondence between the most general supercurrent given in S.M. Kuzenko, J. High Energy Phys. 1004, 022 (2010 and the one obtained eight years ago in M. Magro et al., Ann. Phys. 298, 123 (2002) using the superfield Noether procedure. We apply the Noether procedure to the general N = 1 supersymmetric nonlinear sigma-model and show that it naturally leads to the so-called S-multiplet, revitalized in Z. Komargodski, N. Seiberg, J. High Energy Phys. 1007, 017 (2010).Inspired by a recent work of Komargodski and Seiberg [1], we have presented in [2] the hierarchy of supercurrent multiplets which are associated with the models for linearized 4D N = 1 supergravity classified several years ago in [3]. The most general form of such a multiplet is as follows:Here J αα =J αα denotes the supercurrent, while the chiral superfields χ α , η α and X constitute the so-called multiplet of anomalies. The conservation law (1) incorporates six smaller supercurrent multiplets, of which three include 12 + 12 operators (minimal supercurrents) and the rest describe 16 + 16 components (reducible multiplets). Let us recall the structure of the minimal supercurrent multiplets. The casea e-mail: kuzenko@cyllene.uwa.edu.au describes the famous Ferrara-Zumino multiplet [4]. It corresponds to the old minimal formulation for N = 1 supergravity [5][6][7]. Another choice,corresponds to the new minimal supergravity [8,9] (this supercurrent was studied in [10][11][12]). The third choice,corresponds to the minimal 12 + 12 supergravity formulation which was proposed a few years ago in [13]. Unlike the old minimal and the new minimal theories, this formulation is known at the linearized level only. Among the three reducible supercurrents with 16 + 16 components [2], the most interesting multiplet 1 is singled out by the conditionIt corresponds to the model (36) in [3], which can be shown to be a linearized version of the so-called 16 + 16 supergravity [14,15] known to be reducible [16]. After a 'death sentence' given to this multiplet in the late 1970s, it was recently resurrected by Komargodski and Seiberg [1]. These authors postulated the following supercurrent conservation law:and proved, using laborious component calculations, its consistency in the sense that J αα contains a conserved energymomentum tensor and a conserved supersymmetry current.1 The other reducible supercurrents are obtained by setting either χ α = 0 or X = 0. They appear to be less interesting than the one defined by (5), because the corresponding supergravity formulations are known at the linearized level only.

Complex linear superfields, supercurrents and supergravities

“…The results are 1. the supercurrent multiplets and 2. the necessary X constraint that is required in order to be possible the coupling of the theory with the specific version of supergravity. In section 6, we confirm that the supercurrent multiplets of section 5 conform with the appropriate superspace conservation equation [12][13][14][15], in accordance with the supergravity choice. We do that by deriving the corresponding Bianchi identities and take their on-shell limit.…”

“…New-new-minimal supergravity. Similarly to the previous case, the conservation equation of the new-new-minimal supercurrent is [14,15,17] DαN αα = 2iD 2 D α I . (6.14)…”

“…In a supersymmetric theory, the currents themselves form a supermultiplet which can be encoded in a superfield and this has been used extensively [12][13][14][15]. To determine the supercurrent multiplet of a generic theory we could follow the superfield Noether procedure developed in [16,17].…”

“…However S is not uniquely defined, it has a gauge freedom δS = D 2 F. This is the non-minimal multiplet [14,15]. To make contact with the notation in [13], all the above conservation equations can be organized in the system…”

Imaginary supergravity or Virial supergravity?

“…When a globally supersymmetric theory is scale invariant, it possesses a Virial supercurrent supermultiplet [19][20][21][22]. The multiplet structure is analogous to the R-current supermultiplet in globally R-symmetric theories but we put extra "i"s in various for- 1 Beyond the minimal choice, there has been renewed interest in various non-minimal supercurrent supermultiplets including the S-multiplet [13][14][15][16].…”