On three-dimensional $$ \mathcal{N} $$ = 4 supersymmetry: maximally supersymmetric backgrounds and massive deformations
Year: 2025
Type: article
Abstract: A bstract Using the $$ \textrm{SO}\left(\mathcal{N}\right) $$ SO N superspace formulation for $$ \mathcal{N} $$ N -extended conformal supergravity in three dimensions, we derive all maximally supersymmetric backgrounds in the $$ \mathcal{N} $$ N = 4 case. The specific feature of this choice is that the so-called super Cotton tensor X IJKL = X [ IJKL ] , which exists for $$ \mathcal{N} $$ N ≥ 4, is equivalent to the scalar X defined by X IJKL = ε IJKL 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, p ≥ q , 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, 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 + 2 S ) and ( X – 2 S ) in the left and right sectors of SU(2) L × SU(2) R , respectively. Setting S = 0 leads to the so-called deformed $$ \mathcal{N} $$ N = 4 Minkowski superspace $$ {\mathbbm{M}}_X^{\left.3\right|8} $$ M X 3 8 introduced thirteen years ago. We use projective-superspace techniques to construct general interacting supersymmetric field theories in $$ {\mathbbm{M}}_X^{\left.3\right|8} $$ M X 3 8 and demonstrate that they originate as massive deformations of the following two families of $$ \mathcal{N} $$ N = 4 theories in standard Minkowski superspace $$ {\mathbbm{M}}^{\left.3\right|8} $$ M 3 8 : (i) $$ \mathcal{N} $$ N = 4 superconformal field theories; and (ii) $$ \mathcal{N} $$ N = 4 supersymmetric gauge theories in $$ {\mathbbm{M}}^{\left.3\right|8} $$
Source: Journal of High Energy Physics
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415588447