Abstract
We calculate the transformation laws of the general linear superfield and chiral superfields under supertranslations to all orders in the translation parameters . We use the superfield formalism with complete expansions of the component fields in the coordinate shifts . The results show in particular how a general supertranslation transforms each component field of a supermultiplet into a complete superfield. The results also provide complete parametri-zations of orbits of component fields under supertranslations.
Highlights
Quantum field theories with exact correspondences between bosonic and fermionic helicity states are basic ingredients for superstring theories, but have dominated both theoretical investigations and experimental searches for particle physics beyond the current “Standard Model’’ of particle physics for over three decades now.The minimal version of supersymmetric extensions of the Standard Model extends the generators M, p of the Poincaré group by a set of fermionic generatorsQ and Q in the (1/2,0) and (0,1/2) representations of the proper orthochronous Lorentz group in four dimensions
The results show in particular how a general supertranslation transforms each component field of a supermultiplet into a complete superfield
The first order transformation laws for the components of V have been calculated a long time ago and can be found in many books and review articles on supersymmetry and with our current understanding this is all that is needed to discuss the physical implications of supersymmetry
Summary
Quantum field theories with exact correspondences between bosonic and fermionic helicity states are basic ingredients for superstring theories, but have dominated both theoretical investigations and experimental searches for particle physics beyond the current “Standard Model’’ of particle physics for over three decades now. From a mathematical point of view it is clearly desirable to have the full transformation properties of the general linear multiplet readily available for reference To provide such a reference is the purpose of this paper. To make these results accessible for beginners in supersymmetry, the super-Poincaré algebra and the basic techniques of superspace calculations are reviewed. Chiral superfields provide a particular irreducible representation within the reducible linear multiplet
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