Construction of the effective action in nonanticommutative supersymmetric field theories

Abstract

We develop a general gauge invariant construction of the one-loop effective action for supersymmetric gauge field theories formulated in $\mathcal{N}=1/2$ superspace. Using manifestly covariant techniques (the background superfield method and proper-time representations) adopted to the $\mathcal{N}=1/2$ superspace we show how to define unambiguously the effective action of a matter multiplet (in fundamental and adjoint representations) and the vector multiplet coupled to a background $\mathcal{N}=1/2$ gauge superfield. As an application of this construction we exactly calculate the low-energy one-loop effective action of matter multiplet and SU(2) SYM theory on the Abelian background.

arXiv comment14 pages, LaTeX

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• The number of eigenstates: counting function and heat kernel
• Non(anti)commutative SYM theory: Renormalization in superspace
• On quantum properties of the four-dimensional generic chiral superfield model
• Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States
• N=1/2 Deformations of Chiral Superspaces from New Quantum Poincare and Euclidean Superalgebras
• Renormalizability of non-anticommutative N=(1,1) theories with singlet deformation
• One-loop effective potential in $\mathcal{N}=1/2$ generic chiral superfield model
• Supersymmetric Nambu$-$Jona-Lasinio Model on $\mathcal{N}=1/2$ four-dimensional Non(anti)commutative Superspace
• Instantons in N=1/2 Super Yang-Mills Theory via Deformed Super ADHM Construction
• Vector-multiplet effective action in the non-anticommutative charged hypermultiplet model
• Twisted SUSY: twisted symmetry versus renormalizability
• On the alternative formulation of the three-dimensional noncommutative superspace