Superconformal geometries and local twistors

Howe, Paul; Lindström, Ulf

doi:10.1007/jhep04(2021)140

Cited by 14 publications

(5 citation statements)

References 58 publications

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“…Recently, a new supertwistor formulation was discovered for N -extended conformal supergravity [44]. It is expected to be related to conformal superspace, however relevant technical details have not yet been worked out in the literature.…”

Section: Jhep03(2024)026mentioning

confidence: 99%

$$ \mathcal{N} $$ = 3 conformal superspace in four dimensions

Kuzenko,

Raptakis

2024

J. High Energ. Phys.

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We develop a superspace formulation for $$ \mathcal{N} $$ N = 3 conformal supergravity in four spacetime dimensions as a gauge theory of the superconformal group SU(2, 2|3). Upon imposing certain covariant constraints, the algebra of conformally covariant derivatives $$ {\nabla}_A=\left({\nabla}_a,{\nabla}_{\alpha}^i,{\nabla}_i^{\overset{\cdot }{\alpha }}\right) $$ ∇ A = ∇ a ∇ α i ∇ i α ⋅ is shown to be determined in terms of a single primary chiral spinor superfield, the super-Weyl spinor Wα of dimension +1/2 and its conjugate. Associated with Wα is its primary descendant Bij of dimension +2, the super-Bach tensor, which determines the equation of motion for conformal supergravity. As an application of this construction, we present two different but equivalent action principles for $$ \mathcal{N} $$ N = 3 conformal supergravity. We describe the model for linearised $$ \mathcal{N} $$ N = 3 conformal supergravity in an arbitrary conformally flat background and demonstrate that it possesses U(1) duality invariance. Additionally, upon degauging certain local symmetries, our superspace geometry is shown to reduce to the U(3) superspace constructed by Howe more than four decades ago. Further degauging proves to lead to a new superspace formalism, called SU(3) superspace, which can also be used to describe $$ \mathcal{N} $$ N = 3 conformal supergravity. Our conformal superspace setting opens up the possibility to formulate the dynamics of the off-shell $$ \mathcal{N} $$ N = 3 super Yang-Mills theory coupled to conformal supergravity.

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Section: Jhep03(2024)026mentioning

confidence: 99%

$$ \mathcal{N} $$ = 3 conformal superspace in four dimensions

Kuzenko,

Raptakis

2024

J. High Energ. Phys.

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“…Recently, new supertwistor formulations were discovered for conformal supergravity theories in diverse dimensions 3 ≤ d ≤ 6 [57]. It would be interesting to extend this approach to the d = 2 case.…”

Section: Jhep02(2023)166mentioning

confidence: 99%

Conformal (p, q) supergeometries in two dimensions

Kuzenko

Raptakis

2023

J. High Energ. Phys.

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We propose a superspace formulation for conformal (p, q) supergravity in two dimensions as a gauge theory of the superconformal group OSp0(p|2; ℝ) × OSp0(q|2; ℝ) with a flat connection. Upon degauging of certain local symmetries, this conformal superspace is shown to reduce to a conformally flat SO(p) × SO(q) superspace with the following properties: (i) its structure group is a direct product of the Lorentz group and SO(p) × SO(q); and (ii) the residual local scale symmetry is realised by super-Weyl transformations with an unconstrained real parameter. As an application of the formalism, we describe $$ \mathcal{N} $$ N -extended AdS superspace as a maximally symmetric supergeometry in the p = q ≡ $$ \mathcal{N} $$ N case. If at least one of the parameters p or q is even, alternative superconformal groups and, thus, conformal superspaces exist. In particular, if p = 2n, a possible choice of the superconformal group is SU(1, 1|n) × OSp0(q|2; ℝ), for n ≠ 2, and PSU(1, 1|2) × OSp0(q|2; ℝ), when n = 2. In general, a conformal superspace formulation is associated with a supergroup G = GL× GR, where the simple supergroups GL and GR can be any of the extended superconformal groups, which were classified by Günaydin, Sierra and Townsend. Degauging the corresponding conformal superspace leads to a conformally flat HL× HR superspace, where HL (HR) is the R-symmetry subgroup of GL (GR). Additionally, for the p, q ≤ 2 cases we propose composite primary multiplets which generate the Gauss-Bonnet invariant and supersymmetric extensions of the Fradkin-Tseytlin term.

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“…Supersymmetric models are closely associated to complex geometry in several different ways. To be able to write some extended models in a manifest form superspaces may be extended with a CP 1 at each point thus relating them to twistors [23], conformal supergravity can be formulated in terms of local twistors [14], [15], and supersymmetic nonlinear sigma models is often best formulated in terms of complex superfields and typically have complex target space geometries [28], [1]. This last property is what shall concern us here, although we have to mainly restrict to two-dimensional models with two left and two right going supersymmetries i,e, to 2d, (2, 2) supersymmetry.…”

Section: Introductionmentioning

confidence: 99%

$2d$ Sigma Models and Geometry

Lindström¹

2022

Preprint

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Supersymmetric nonlinear sigma models have target spaces that carry interesting geometry. The geometry is richer the more supersymmetries the model has. The study of models with two dimensional world sheets is particularly rewarding since they allow for torsionful geometries. In this review I describe and exemplify the relation of 2d supersymmetry to Riemannian, complex, bihermitian, (p, q) hermitean, Kähler, hyperkähler, generalised geometry and more. 1

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Superconformal geometries and local twistors

Cited by 14 publications

References 58 publications

$$ \mathcal{N} $$ = 3 conformal superspace in four dimensions

$$ \mathcal{N} $$ = 3 conformal superspace in four dimensions

Conformal (p, q) supergeometries in two dimensions

$2d$ Sigma Models and Geometry

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