The Minkowski and conformal superspaces

Fioresi, R.; Lledó, M. A.; Varadarajan, V. S.

doi:10.1063/1.2799262

Cited by 38 publications

(79 citation statements)

References 12 publications

(44 reference statements)

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“…[17]). A supersymmetric version of the tractor calculus can be found in [18], and a related superembedding formalism for free fields has appeared in ref. [19].…”

Section: While It Is Not Yet Known If Such General Principles Are Sufmentioning

confidence: 99%

Superembedding methods for 4DN=1SCFTs

2012

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We extend the SO(4, 2) covariant lightcone embedding methods of four-dimensional CFTs to N = 1 superconformal field theory (SCFT). Manifest superconformal SU (2, 2|1) invariance is achieved by realizing 4D superconformal space as a surface embedded in the projective superspace spanned by certain complex chiral supermatrices. Because SU (2, 2|1) acts linearly on the ambient space, the constraints on correlators implied by superconformal Ward identities are automatically solved in this formalism. Applications include new, compact expressions for correlation functions containing one anti-chiral superfield and arbitrary chiral superfield insertions, and manifestly invariant expressions for the superconformal cross-ratios that parametrize the four-point function of two chiral and two anti-chiral fields. Superconformal expressions for the leading singularities in the OPE of chiral and anti-chiral operators are also given. Because of covariance, our expressions should hold in any superconformally flat background, e.g., AdS 4 or R × S 3 .

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“…[17]). A supersymmetric version of the tractor calculus can be found in [18], and a related superembedding formalism for free fields has appeared in ref. [19].…”

Section: While It Is Not Yet Known If Such General Principles Are Sufmentioning

confidence: 99%

Superembedding methods for 4DN=1SCFTs

2012

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“…. Technically this is realized, along the line of [17,18,19,20,21] (see also [22,23,24] for a generalization to the super setting) and [25,26]. We also speculate on the interpretation of the "new" parameter ℓ , showing that the product of two ℓ commuting (or linked) quantum planes (or quantum spinors in the physical language [27]) reproduces the deformed algebra of the complex q-linked Minkowski space.…”

Section: Introductionmentioning

confidence: 80%

The q-linked complex Minkowski space, its real forms and deformed isometry groups

Fioresi

Latini

Marrani

2019

Int. J. Geom. Methods Mod. Phys.

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We establish duality between real forms of the quantum deformation of the 4-dimensional orthogonal group studied by Fioresi et al. in [15] and the classification work made by Borowiec et al. in [12]. Classically these real forms are the isometry groups of R 4 equipped with Euclidean, Kleinian or Lorentzian metric. A general deformation, named q-linked, of each of these spaces is then constructed, together with the coaction of the corresponding isometry group.

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“…These sheafs can be glued conveniently, the procedure being similar to the one used for standard projective space. In this way we obtain the supervariety P m|n representing the functor (2). For a detailed proof of this fact, see Refs.…”

Section: Definition 24mentioning

confidence: 89%

“…The Levi subgroup G 0 is the Lorentz group times dilations. If one represents an element in the Grassmannian Gr (2,4) in terms of a 4 × 2-matrix whose columns are the basis vectors of the 2-plane, the big cell is characterized in terms of matrices with the minor d 12 = 0. By a change of basis one can always bring such matrix to a standard form…”

Section: Parabolic (Super)geometriesmentioning

confidence: 99%

The Segre embedding of the quantum conformal superspace

Fioresi

Latini

Lledó

et al. 2018

Advances in Theoretical and Mathematical Physics

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In this paper study the quantum deformation of the superflag Fl(2|0, 2|1, 4|1), and its big cell, describing the complex conformal and Minkowski superspaces respectively. In particular, we realize their projective embedding via a generalization to the super world of the Segre map and we use it to construct a quantum deformation of the super line bundle realizing this embedding. This strategy allows us to obtain a description of the quantum coordinate superring of the superflag that is then naturally equipped with a coaction of the quantum complex conformal supergroup SL q (4|1).

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The Minkowski and conformal superspaces

Cited by 38 publications

References 12 publications

Superembedding methods for 4DN=1SCFTs

Superembedding methods for 4DN=1SCFTs

The q-linked complex Minkowski space, its real forms and deformed isometry groups

The Segre embedding of the quantum conformal superspace

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