2025/04/29 by Kuzenko, Sergei M., Raptakis, Emmanouil S. N., Samsonov, Igor B. +1
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2504.20712
Using the SO (\cal N) superspace formulation for \cal N-extended conformal supergravity in three dimensions, we derive all maximally supersymmetric backgrounds in the \cal N =4 case. The specific feature of this choice is that the so-called super Cotton tensor XIJKL = X[IJKL], which exists for \cal N ≥ 4, is equivalent to the scalar X defined by XIJKL = εIJKL X. This scalar may be used as a deformation parameter. In the family of (p,q) anti-de Sitter (AdS) superspaces with p+q=4, it is known that X≠ 0 exists only if p=4 and q=0. In general, the (4,0) AdS superspaces are characterised by the structure group SL(2,\mathbb R) × SO (4) and their geometry is determined by two constant parameters, S and X, of which the former determines the AdS curvature, while the R-symmetry curvature is determined by the parameters (X+2S) and (X-2S) in the left and right sectors of SU(2)\rm L × SU(2)\rm R, respectively. Setting S=0 leads to the so-called deformed \cal N=4 Minkowski superspace \mathbb M3|8X introduced thirteen years ago. We construct general interacting supersymmetric field theories in \mathbb M3|8X and demonstrate that they originate as massive deformations of the following two families of \cal N =4 theories in standard Minkowski superspace \mathbb M3|8: (i) \cal N=4 superconformal field theories; and (ii) \cal N=4 supersymmetric gauge theories in \mathbb M3|8 which are not superconformal but possess the R-symmetry group SU(2)\rm L × SU(2)\rm R. Extensions of the theories in (ii) to \mathbb M3|8X necessarily contain Chern-Simons terms at the component level. We also demonstrate the generation of topologically massive \cal N=4 supersymmetric gauge theories from radiative corrections in the hypermultiplet sector.