On short and semi-short representations for four-dimensional superconformal symmetry

By F. Dolan, H. Osborn. 2002

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Abstract Possible short and semi-short representations for N =2 and N =4 superconformal symmetry in four dimensions are discussed. For N =4 the well known short supermultiplets whose lowest dimension conformal primary operators correspond to 1 2 -BPS or 1 4 -BPS states and are scalar fields belonging to the SU(4) R-symmetry representations [0,p,0] and [q,p,q] and having scale dimension Δ=p and Δ=2q+p, respectively, are recovered. The representation content of semi-short multiplets, which arise at the unitarity threshold for long multiplets, is discussed. It is shown how, at the unitarity threshold, a long multiplet can be decomposed into four semi-short multiplets. If the conformal primary state is spinless one of these becomes a short multiplet. For N =4 a 1 4 -BPS multiplet need not have a protected dimension unless the primary state belongs to a [1,p,1] representation.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e6322881ca5327db53cc58866c9d68e403d2143c

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Citations in the corpus

Elliptic Hypergeometry of Supersymmetric Dualities (2009, neutral): “The commutation relations have the form [25] [Mab, Pc] = i(ηacPb − ηbcPa), [Mab, Kc] = i(ηacKb − ηbcKa), [Mab,Mcd] = i(ηacMbd − ηbcMad − ηadMbc + ηbdMac), (3.”
Infinite Chiral Symmetry in Four Dimensions (2013, methodology): “where we follow the conventions of [28] for r, and which obey the commutation relations”
S-duality and 2d topological QFT (2009, neutral): “2 (2)Our normalization for the R-symmetry charges is as in [31] and differs from [25]: Rhere = Rthere/2, rhere = rthere/2.”
Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations (2015, background): “Name [35] Primary field quantum numbers Null states AR,r(j,̃) ∆ > 2R+ 2 + |r + j − ̃|+ j + ̃ none CR,r(j,̃) ∆ = 2R+ 2− r + 2̃, r < ̃− j (B.”
The superconformal index of the E6 SCFT (2010, methodology): “(5)Our normalization convention for the R-symmetry charges is as in [15] and differs from [6]: Rhere = Rthere/2, rhere = rthere/2.”
An Index for 4 Dimensional Super Conformal Theories (2005, methodology): “In [20], Dolan and Osborn, performed a comprehensive tabulation of short representations of the d = 4 superconformal algebras.”
Supersymmetric states of N=4 Yang-Mills from giant gravitons (2006, neutral): “13 2.6 U(3) charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14”
All tree-level correlators in AdS5×S5 supergravity: hidden ten-dimensional conformal symmetry (2018, methodology): “Using the general formula for the tensor product of SU(4) representations (see [44, 45]): [ 0, p, 0 ] × [ 0, q, 0 ] = p ∑”
Gauge Theories and Macdonald Polynomials (2011, methodology): “The shortening conditions for the N = 2 superconformal algebra were studied in [80, 81, 82].”
Higher Spin Symmetry and N = 4 SYM (2004, methodology): “Anomalous dimensions can be computed either by old-fashion QFT methods [32,25,26,33,21,22] or by brand-new techniques based on the identification of the planar dilatation operator [34] with the Hamiltonian of an integrable super-spin chain [35–37].”
How to succeed at holographic correlators without really trying (2017, methodology): “, [47] for a complete tabulation of the multiplet).”
On Four-Point Functions of Half-BPS Operators in General Dimensions (2004, methodology): “Following an approach like that for construction of superconformal multiplets in [34] based on using the Racah Speisser algorithm (described in [35]), we show how we may verify that the conformal partial wave expansion results for long multiplets are consistent with representation theory.”
Superconformal Ward identities and their solution (2004, background): “67) The necessary operators here correspond to table 5 and table 1 in [22].”
On instantons as Kaluza-Klein modes of M5-branes (2011, neutral): “11) of [60].”
The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability (2004, background): “In perturbation theory multiplets close to the unitarity bound have some special features, see for example [8, 10, 92].”
Applications of the superconformal index for protected operators and q-hypergeometric identities to N=1 dual theories (2008, neutral): “= 0 , (A.6b) which are referred to as semi-short [ 25 ].”