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Ferrara, S.; Sokatchev, E.

doi:10.1023/a:1007641619266

Cited by 38 publications

(27 citation statements)

References 27 publications

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“…It is easy to see that for the massless cases given in (3.20) one has: 27) which is indeed negative for j 2 = 0, 1 2 and non-negative for j 2 ≥ 1. In fact, the finite-dimensional irrep, related to a massless case with j 2 ≥ 1, has dimension [45]:…”

Section: Characters Of the Even Subalgebramentioning

confidence: 96%

“…The UIRs of G are realized as irreducible components of ERs, and then they coincide with the usually used superfields in indexless notation. This construction is canonical, yet we should mention that some of the resulting superspaces were obtained in the papers [24], [25], [26], [27], [28], using the notions of 'harmonic superspace analyticity' and 'Grassmann analyticity'. The relation between the latter approach and ours were commented on in [4], [18], [17].…”

Section: The Settingmentioning

confidence: 99%

“…These UIRs are called long in the modern literature, cf., e.g., [36], [37], [27], [28], [38], [39], [40], [41]. Analogously, we shall use for the cases when d = d max , i.e., (2.24a), the terminology of semi-short UIRs, introduced in [36], [37], [28], while the cases (2.24b, c, d) are also called short UIRs, cf., e.g., [37], [27], [28], [38], [39], [40], [41].…”

Section: Singular Vectors and Invariant Submodules At The Unitary Redmentioning

confidence: 99%

“…As in the previous subsection we shall use for the cases when d = d max , i.e., (2.34a), also the terminology of semi-short UIRs, [36], [28], while the cases (2.34b, c, d) shall also be called short UIRs [27], [28], [38], [39], [40], [41].…”

Section: The Factorized Verma Modulesṽmentioning

confidence: 99%

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Explicit character formulae for positive energy unitary irreducible representations ofD= 4 conformal supersymmetry

Dobrev¹

2013

J. Phys. A: Math. Theor.

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This paper continues the project of constructing the character formulae for the positive energy unitary irreducible representations of the N -extended D = 4 conformal superalgebras su(2, 2/N ). In the first paper we gave the bare characters which represent the defining odd entries of the characters. Now we give the full explicit character formulae for N = 1 and for several important examples for N = 2 and N = 4.

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Section: Characters Of the Even Subalgebramentioning

confidence: 96%

Section: The Settingmentioning

confidence: 99%

Section: Singular Vectors and Invariant Submodules At The Unitary Redmentioning

confidence: 99%

Section: The Factorized Verma Modulesṽmentioning

confidence: 99%

See 2 more Smart Citations

Explicit character formulae for positive energy unitary irreducible representations ofD= 4 conformal supersymmetry

Dobrev¹

2013

J. Phys. A: Math. Theor.

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“…To reduce to the usual 11 independent complex parameters of pure spinors, we further impose the following two covariant constraints u a Iv bI = 0 , λ α a ǫ αβ ǫ ab λ β b +λα a ǫαβǫ abλβ b = 0 . S(U(2)×U(2)) used in [7](see also [11] and [9]). The restriction of U (2) × U (2) to the subgroup S(U (2) × U (2)) is due to second constraint of (2.4).…”

Section: The Decomposition In (22) Is Left Invariant By the Gauge Trmentioning

confidence: 99%

Harmonic superspaces from superstrings

Grassi

Nieuwenhuizen

2004

Physics Letters B

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We derive harmonic superspaces for N = 2, 3, 4 SYM theory in four dimensions from superstring theory. The pure spinors in ten dimensions are dimensionally reduced and yield the harmonic coordinates. Two anticommuting BRST charges implement Grassmann analyticity and harmonic analyticity. The string field theory action produces the action and field equations for N=3 SYM theory in harmonic superspace.Stony Brook, 2/24/2004

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Invariant differential operators for non-compact Lie algebras parabolically related to conformal Lie algebras

Dobrev

2013

J. High Energ. Phys.

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In the present paper we continue the project of systematic construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we call 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduce the new notion of parabolic relation between two non-compact semisimple Lie algebras G and G ′ that have the same complexification and possess maximal parabolic subalgebras with the same complexifica-tion. Thus, we consider the exceptional algebra E 7(7) which is parabolically related to the CLA E 7(−25) , the parabolic subalgebras including E 6(6) and E 6(−26). Other interesting examples are the orthogonal algebras so(p, q) all of which are parabolically related to the conformal algebra so(n, 2) with p + q = n + 2, the parabolic subalgebras including the Lorentz subalgebra so(n − 1, 1) and its analogs so(p − 1, q − 1). We consider also E 6(6) and E 6(2) which are parabolically related to the hermitian symmetric case E 6(−14) , the parabolic subalgebras including real forms of sl(6). We also give a formula for the number of representations in the main multiplets valid for CLAs and all algebras that are parabolically related to them. In all considered cases we give the main multiplets of indecomposable elementary representations including the necessary data for all relevant invariant differential operators. In the case of so(p, q) we give also the reduced multiplets. We should stress that the multiplets are given in the most economic way in pairs of shadow fields. Furthermore we should stress that the classification of all invariant differential operators includes as special cases all possible conservation laws and conserved currents, unitary or not.

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Untitled

Abstract: We consider the harmonic superspaces associated to SU (2, 2/N )

Cited by 38 publications

References 27 publications

Explicit character formulae for positive energy unitary irreducible representations ofD= 4 conformal supersymmetry

Explicit character formulae for positive energy unitary irreducible representations ofD= 4 conformal supersymmetry

Harmonic superspaces from superstrings

Invariant differential operators for non-compact Lie algebras parabolically related to conformal Lie algebras

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