Abstract
For extended mathcal{N} ≤ 8 supersymmetry we classify all possible gauge groups for a scalar multiplet allowed by the algebras of global and local supersymmetry in three dimensions. A detailed discussion of supersymmetry enhancement is included. For the corresponding topologically massive gravity with negative cosmological constant the mass of the graviton is determined algebraically as a function of mathcal{N} and the possible gauge couplings.
Highlights
Introduction and summarySuperconformal Chern-Simons theories play an important role as conformal field theories describing aspects of M2-branes in string theory, as was suggested in [1] and became clear with the constructions of the BLG [2,3,4,5] and ABJM [6, 7] models with gauge groups SO(4) and U(M ) × U(N ), inheriting N = 8 and N = 6 superconformal symmetry respectively
For extended N ≤ 8 supersymmetry we classify all possible gauge groups for a scalar multiplet allowed by the algebras of global and local supersymmetry in three dimensions
These findings were explained as constraints on possible gauge groups from manifest supersymmetry through superspace approaches for N = 6 and 8 in [12, 13] and [14], and for N = 4 and 5 in [15] and [16]
Summary
Focusing on the situation in flat superspace we find a collection of admissible gauge groups for N = 4 constituting, in a sequence of increasing N , the first occurrence of a restriction on possible gauge symmetries for fundamental and bifundamental matter (we note in passing that the spin(7) implies G2 gauging, as the subgroup preserving some fixed compensator.) The same restriction appears for N = 5 This can be understood by noticing that an N = 4 Clifford representation naturally exhibits the same properties as the chiral one, since the left- and right-handed components transform under different factors of spin(4) = SU(2) × SU(2), while on the other hand, the N = 4 Clifford representation just coincides with an implementation of the N = 5 spin group USp(4). The similarity between N = 7 and 8 is supported by the existence of real and orthogonal representations of their spin groups In this conformal case, the gravitationally coupled N = 7 and 8 theories are different ( they admit the same gauge groups), which may be worth pointing out in view of results for Poincare supergravity In the subsequent sections we analyse each model with N -extended supergravity, leading to the results outlined above, as well as obtaining on-shell equations for the gauge and supergravity sectors
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