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Abstract: We review the non-anticommutative Q-deformations of N=1,1 supersymmetrictheories in four-dimensional Euclidean harmonic superspace. These deformationspreserve chirality and harmonic Grassmann analyticity. The associated fieldtheories arise as a low-energy limit of string theory in specific backgroundsand generalize the Moyal-deformed supersymmetric field theories. Acharacteristic feature of the Q-deformed theories is the half-breaking ofsupersymmetry in the chiral sector of the Euclidean superspace. Our main focusis on the chiral singlet Q-deformation, which is distinguished by preservingthe SO4 Spin4 ``Lorentz- symmetry and the SU2 R-symmetry. We present thesuperfield and component structures of the deformed N=1,0 supersymmetricgauge theory as well as of hypermultiplets coupled to a gauge superfield:invariant actions, deformed transformation rules, and so on. We discuss quantumaspects of these models and prove their renormalizability in the abelian case.For the charged hypermultiplet in an abelian gauge superfield background weconstruct the deformed holomorphic effective action.

Autor: I.L. Buchbinder, E.A. Ivanov, O. Lechtenfeld, I.B. Samsonov, B.M. Zupnik


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