Young supertableaux of the basic Lie superalgebras

Hurni, Jean-Pierre

doi:10.1088/0305-4470/20/17/016

Cited by 23 publications

(11 citation statements)

References 33 publications

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“…But in our situation, we want to make use of the "notation of the highest weight" interpretation of the Young supertabulaux. So we use the proposal [49] and its extension [51]. The correspondence between the two different representations are discussed in [49].…”

Section: B Nonlinear Terms In Super-w ∞ [λ]mentioning

confidence: 99%

Symmetries of holographic super-minimal models

Hanaki¹,

Peng²

2013

J. High Energ. Phys.

129

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We compute the asymptotic symmetry of the higher-spin supergravity theory in AdS 3 and obtain an infinite-dimensional non-linear superalgebra, which we call the super-W ∞ [λ] algebra.According to the recently proposed supersymmetric duality between higher-spin supergravity in an AdS 3 background and the 't Hooft limit of the N = 2 CP n Kazama-Suzuki model on the boundary, this symmetry algebra should agree with the 't Hooft limit of the chiral algebra of the CFT, SW n . We provide two nontrivial checks of the duality. By comparing the algebras, we explicitly match the lowest-spin commutation relations in the super-with the corresponding commutation relations in the 't Hooft limit on the CFT side. We also consider the degenerate representations of the two algebras and find that the spectra of the chiral primary fields are identical.

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Section: B Nonlinear Terms In Super-w ∞ [λ]mentioning

confidence: 99%

Symmetries of holographic super-minimal models

Hanaki¹,

Peng²

2013

J. High Energ. Phys.

129

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“…, k n ), where the number of labels n can take various values, but for our discussion won't extend beyond n = 3. The interested reader can find out more about the physical significance of the SYT and their corresponding labels in the context of the ABJM theory in [26] (see [27,28,29,30,31,32] for a more general discussion). Here we will use the SYT labels as a significantly more compact formalism for describing multiplets than the Cartan charges.…”

Section: Preliminariesmentioning

confidence: 99%

Two-loop spectroscopy of short ABJM operators

Παπαθανασίου

Spradlin

2010

J. High Energ. Phys.

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We study the spectrum of anomalous dimensions of short operators in planar ABJM theory at two loops. Specifically we develop a method for solving the OSp(6|4) Bethe ansatz equations for a certain class of unpaired length-4 states with arbitrarily high number of excitations, and apply it to identify three new sequences of rational eigenvalues. Results for low-lying paired states in the OSp(4|2) sector are obtained by direct diagonalization of the spin chain Hamiltonian. We also study the SL(2|1) sector and identify the set of states that corresponds to the SL(2)-like Bethe ansatz of Gromov and Vieira. Finally we extend part of our analysis to length-6 operators.

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“…There exists a rich literature on super-Young tableaux [36,37,38,39,40,41] and their applications (see for example [42,35,29,32,33]), so here we'll just mention a few intuitive examples. To any contravariant superoscillator, namely the ones of the second row of (2.22), there corresponds single (slashed) SYT .…”

Section: Osp(6|4) and Super-young Tableauxmentioning

confidence: 99%

The morphology of 𝒩 = 6 Chern-Simons theory

Παπαθανασίου¹,

Spradlin²

2009

J. High Energy Phys.

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We tabulate various properties of the 'language' of N = 6 Chern-Simons Theory, in the sense of Polyakov. Specifically we enumerate and compute character formulas for all syllables of up to four letters, i.e. all irreducible representations of OSp(6|4) built from up to four fundamental fields of the ABJM theory. We also present all tensor product decompositions for up to four singletons and list the (cyclically invariant) four-letter words, which correspond to single-trace operators of length four. As an application of these results we use the two-loop dilatation operator to compute the leading correction to the Hagedorn temperature of the weakly-coupled planar ABJM theory on R × S 2 .

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Young supertableaux of the basic Lie superalgebras

Cited by 23 publications

References 33 publications

Symmetries of holographic super-minimal models

Symmetries of holographic super-minimal models

Two-loop spectroscopy of short ABJM operators

The morphology of 𝒩 = 6 Chern-Simons theory

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