Non-singlet Q-deformation of the N=(1,1) gauge multiplet in harmonic superspace

Abstract

We study a non-anticommutative chiral non-singlet deformation of the N=(1,1) abelian gauge multiplet in Euclidean harmonic superspace with a product ansatz for the deformation matrix, C^{(αβ)}_{(ik)} = c^{(αβ)}b_{(ik)}. This allows us to obtain in closed form the gauge transformations and the unbroken N=(1,0) supersymmetry transformations preserving the Wess-Zumino gauge, as well as the bosonic sector of the N=(1,0) invariant action. As in the case of a singlet deformation, the bosonic action can be cast in a form where it differs from the free action merely by a scalar factor. The latter is now given by \cosh^2 (2\barϕ\sqrt{c^2 b^2}}), with \barϕbeing one of two scalar fields of the N=(1,1) vector multiplet. We compare our results with previous studies of non-singlet deformations, including the degenerate case b^2=0 which preserves the N=(1,1/2) fraction of N=(1,1) supersymmetry.

1+30 pages. Eq. (3.36) corrected. Extended concluding remarks. Version to appear in NPB

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• Deformation of Super Yang-Mills Theories in R-R 3-form Background
• Computing the Scalar Field Couplings in 6D Supergravity
• Noncommutative Superspace and Super Heisenberg Group
• Non-singlet Q-deformed N=(1,0) and N=(1,1/2) U(1) actions
• Renormalizability of non-anticommutative N=(1,1) theories with singlet deformation
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Instanton Calculus in R-R 3-form Background and Deformed N=2 Super Yang-Mills Theory
• Gauge theory in deformed N=(1,1) superspace
• Real and pseudoreal forms of D=4 complex Euclidean (super)algebras and super-Poincare / super-Euclidean r-matrices
• AdS/CFT Duality for Non-Anticommutative Supersymmetric Gauge Theory
• Instantons in N=1/2 Super Yang-Mills Theory via Deformed Super ADHM Construction
• Morita Equivalence of Noncommutative Supertori
• Vector-multiplet effective action in the non-anticommutative charged hypermultiplet model