Superfield formulation of the simplest three-dimensional gauge theories and conformal supergravities

We study implications of N = 4 superconformal symmetry in three dimensions, thus extending our earlier results in [1] devoted to the N ≤ 3 cases. We show that the three-point function of the supercurrent in N = 4 superconformal field theories contains two linearly independent forms. However, only one of these structures contributes to the three-point function of the energy-momentum tensor and the other one is present in those N = 4 superconformal theories which are not invariant under the mirror map. We point out that general N = 4 superconformal field theories admit two inequivalent flavour current multiplets and show that the three-point function of each of them is determined by one tensor structure. As an example, we compute the two-and three-point functions of the conserved currents in N = 4 superconformal models of free hypermultiplets. We also derive the universal relations between the coefficients appearing in the two-and threepoint correlators of the supercurrent and flavour current multiplets in all superconformal theories with N ≤ 4 supersymmetry. Our derivation is based on the use of Ward identities in conjunction with superspace reduction techniques.

Section: N = 2 Superconformal Theoriesmentioning

confidence: 99%

Implications of N = 4 $$ \mathcal{N}=4 $$ superconformal symmetry in three spacetime dimensions

Buchbinder

Kuzenko

Samsonov

2015

“…The conformal N = 2 supergravity, and the two-derivative invariants were considered in [8][9][10][11]. Off-shell matter-coupled suprgravity theories were investigated in the superspace framework in [12][13][14][15].…”

Section: Jhep02(2015)125mentioning

confidence: 99%

“…Namely, QQ commutation leads to a translation parameter 8) which can be shown to be identical to the usual translation parameter 9) by using (A.7). The charge conjugation of a spinor is defined by λ C = B −1 λ * = (Bλ) * and the complex conjugation of bilinears are 11) where the charge conjugation of matrices are determined by (Γ 1 Γ 2 ) C = Γ C 1 Γ C 2 and γ C µ = γ µ .…”

Section: Jhep02(2015)125mentioning

confidence: 99%

Massive N $$ \mathcal{N} $$ = 2 supergravity in three dimensions

Alkaç

Basanisi

Bergshoeff

et al. 2015

There exists two distinct off-shell N = 2 supergravities in three dimensions. They are also referred to as N = (1, 1) and N = (2, 0) supergravities, and they arise from the coupling of the Weyl multiplet to a compensating scalar or vector multiplet, respectively, followed by fixing of conformal symmetries. The N = (p, q) terminology refers to the underlying anti-de Sitter superalgebras OSp(2, p)⊕OSp(2, q) with R-symmetry group SO(p) × SO(q). We construct off-shell invariants of these theories up to fourth order in derivatives. As an application of these results, we determine the special combinations of the N = (1, 1) invariants that admit anti-de Sitter vacuum solution about which there is a ghost-free massive spin-2 multiplet of propagating modes. We also show that the N = (2, 0) invariants do not allow such possibility.

“…We start with a brief description of the N = 2, d3 super Chern-Simons theory [27], [28], [29] . The constrained geometry of N = 2 supergauge field is formulated in R 3|4 superspace with coordinates z M = {x m , θ α ,θ α } 2 in terms of the gauge covariant derivatives…”

Section: N = 2 D3 Superfield Modelsmentioning

confidence: 99%

The background field method for $ \mathcal{N} = {2} $ , d3 super Chern-Simons-matter theories

Buchbinder

Плетнев

2011