Abstract
For all types of N=4 anti-de Sitter (AdS) supersymmetry in three dimensions, we construct manifestly supersymmetric actions for Abelian vector multiplets and explain how to extend the construction to the non-Abelian case. Manifestly N=4 supersymmetric Yang-Mills (SYM) actions are explicitly given in the cases of (2,2) and critical (4,0) AdS supersymmetries. The N=4 vector multiplets and the corresponding actions are then reduced to (2,0) AdS superspace, in which only N=2 supersymmetry is manifest. Using the off-shell structure of the N=4 vector multiplets, we provide complete N=4 SYM actions in (2,0) AdS superspace for all types of N=4 AdS supersymmetry. In the case of (4,0) AdS supersymmetry, which admits a Euclidean counterpart, the resulting N=2 action contains a Chern-Simons term proportional to q/r, where r is the radius of AdS_3 and q is the R-charge of a chiral scalar superfield. The R-charge is a linear inhomogeneous function of X, an expectation value of the N=4 Cotton superfield. Thus our results explain the mysterious structure of N=4 supersymmetric Yang-Mills theories on S^3 discovered in arXiv:1401.7952. In the case of (3,1) AdS supersymmetry, which has no Euclidean counterpart, the SYM action contains both a Chern-Simons term and a chiral mass-like term. In the case of (2,2) AdS supersymmetry, which admits a Euclidean counterpart, the SYM action has no Chern-Simons and chiral mass-like terms.
Highlights
Samsonov and Sorokin [1] have constructed N = 4 supersymmetric Yang-Mills (SYM) theories on S3, both in terms of N = 2 superfields and component fields
Using the off-shell structure of the N = 4 vector multiplets, we provide complete N = 4 SYM actions in (2,0) anti-de Sitter (AdS) superspace for all types of N = 4 AdS supersymmetry
In the Abelian case, these theories were described within the manifestly N = 4 supersymmetric setting as well as in (2,0) AdS superspace where only N = 2 supersymmetry is manifest
Summary
In a curved N = 4 superspace [6], they may be described in terms of gauge-invariant field strengths, W ij = W ji = Wij and Wij = Wji = Wij, which transform under the left and right subgroups of the supergravity R-symmetry group SU(2)L × SU(2)R, respectively, and obey the inequivalent analyticity constraints. To describe the dynamics of an Abelian left vector multiplet in a given N = 4 AdS superspace, it suffices to make use of the right action only, such that SL = 0. (4.2) and (4.4) may be rewritten in the form: S[VR] This is similar to the action for the Abelian N = 2 vector multiplet in four dimensions constructed first in the rigid supersymmetric case [18] (see [19]) and later in supergravity [20].
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