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Register a new userSigma models with off-shell N=(4,4) supersymmetry and noncommuting complex structures
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We describe the conditions for extra supersymmetry in N=(2,2) supersymmetric nonlinear sigma models written in terms of semichiral superfields. We find that some of these models have additional off-shell supersymmetry. The (4,4) supersymmetry introduces geometrical structures on the target-space which are conveniently described in terms of Yano f-structures and Magri-Morosi concomitants. On-shell, we relate the new structures to the known bi-hypercomplex structures.
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We discuss the conditions for extra supersymmetry of the N=(2,2) supersymmetric vector multiplets described in arXiv:0705.3201 [hep-th] and in arXiv:0808.1535 [hep-th]. We find (4,4) supersymmetry for the semichiral vector multiplet but not for the Large Vector Multiplet.
We discuss additional supersymmetries for N = (2, 2) supersymmetric non-linear sigma models described by left and right semichiral superfields.
We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral superfields. Several superspace proofs of the folklore statement that N=3 supersymmetry implies N=4 are presented both in the on-shell and off-shell settings. We also elaborate on (super)twistor realisations for (super)manifolds on which the three-dimensional N-extended superconformal groups act transitively and which include Minkowski space as a subspace.
We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N=2, the R-symmetry is SO(2)times SO(1,1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N=2 models with H-flux so that the target geometry is generalised Kahler, it is necessary to work with a complexification of the sigma models. These issues are related to the obstructions to the existence of non-trivial twisted chiral superfields in Euclidean superspace.
We continue the search for rules that govern when off-shell 4D, $cal N$ = 1 supermultiplets can be combined to form off-shell 4D, $cal N$ = 2 supermultiplets. We study the ${mathbb S}_8$ permutations and Height Yielding Matrix Numbers (HYMN) embedded within the adinkras that correspond to these putative 4D, $cal N$ = 2 supermultiplets off-shell supermultiplets. Even though the HYMN definition was designed to distinguish between the raising and lowering of nodes in one dimensional valises supermultiplets, they are shown to accurately select out which combinations of off-shell 4D, $cal N$ = 1 supermultiplets correspond to off-shell 4D, $cal N$ = 2 supermultiplets. Only the combinations of the chiral + vector and chiral + tensor are found to have valises in the same class. This is consistent with the well known structure of 4D, $cal N$ = 2 supermultiplets.
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