Gauge theory in deformed $$ \mathcal{N} $$ = (1, 1) superspace
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o the memory of Julius Wess
Gauge Theory in Deformed = (1, 1) Superspace¶ I. L. Buchbindera, b, E. A. Ivanovc, O. Lechtenfeldd, I. B. Samsonovd, e, and B. M. Zupnikc a Dept. of Chemistry and Physics, University of North Carolina, Pembroke, NC 28372, USA b Dept. of Theoretical Physics, Tomsk State Pedagogical University, Tomsk, 634041 Russia
c Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia d Institut für Theoretische Physik, Leibniz Universität Hannover, 30167 Hannover, Germany e Laboratory of Mathematical Physics, Tomsk Polytechnic University, Tomsk, 634050 Russia
e-mail: [email protected]; [email protected]; eivanov, [email protected]; lechtenf, [email protected]; [email protected] Abstract—We review the non-anticommutative Q-deformations of = (1, 1) supersymmetric theories in fourdimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) ~ Spin(4) “Lorentz” symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed = (1, 0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the Abelian case. For the charged hypermultiplet in an Abelian gauge superfield background we construct the deformed holomorphic effective action. PACS numbers: 12.60.Jv DOI: 10.1134/S1063779608050031
1. INTRODUCTION By now, the concept of supersymmetry has been organically incorporated into modern high-energy theoretical physics. Originally, it was introduced at the mathematical level as a possible kind of new symmetry that extends the standard space–time symmetries by spinorial generators and relates bosons and fermions. Since then, the consequences of the supersymmetry hypothesis for particle physics has proved so fruitful that today it is hardly possible to doubt its validity. At present, the quest for supersymmetric partners of the known elementary particles is one of the main occupations of the forthcoming LHC experiments.1 Let us mention the most impressive achievements of supersymmetry. First of all, it yields a unified setup for describing bosons and fermions. In the Standard Model, it suggests a natural solution of the hierarchy problem. In grand unification models, it predicts the single-point meeting of the three basic running couplings (see e.g. [2]) and solves the problem of the proton lifetime. Finally, the most popular candidate for unifying
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