W-algebras and their representations

Watts, Gérard

doi:10.1007/bfb0105278

Cited by 12 publications

(7 citation statements)

References 48 publications

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“…What we are advocating here is the classical analogue of what happens for the quantum W 3 for c = −22/5 [28]. Let us remind the reader of the quantum version of the W 3 algebra is.…”

Section: The Solutionmentioning

confidence: 99%

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Topologically massive higher spin gravity

Bagchi

Lal

Saha

et al. 2011

J. High Energ. Phys.

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Abstract:We look at the generalisation of topologically massive gravity (TMG) to higher spins, specifically spin-3. We find a special "chiral" point for the spin-three, analogous to the spin-two example, which actually coincides with the usual spin-two chiral point. But in contrast to usual TMG, there is the presence of a non-trivial trace and its logarithmic partner at the chiral point. The trace modes carry energy opposite in sign to the traceless modes. The logarithmic partner of the traceless mode carries negative energy indicating an instability at the chiral point. We make several comments on the asymptotic symmetry and its possible deformations at this chiral point and speculate on the higher spin generalisation of LCF T 2 dual to the spin-3 massive gravity at the chiral point.

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“…What we are advocating here is the classical analogue of what happens for the quantum W 3 for c = −22/5 [28]. Let us remind the reader of the quantum version of the W 3 algebra is.…”

Section: The Solutionmentioning

confidence: 99%

“…This shifts the overall quadratic coefficient of the quadratic term from 16 5c → 16 5c+22 in (5.1). As is obvious, c = −22/5 represents a blowing up of the quantum W 3 algebra and [28] prescribes a similar procedure to what we have outlined above.…”

Section: The Solutionmentioning

confidence: 99%

Topologically massive higher spin gravity

Bagchi

Lal

Saha

et al. 2011

J. High Energ. Phys.

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show abstract

“…The construction introduced a new type of extended conformal symmetry, and gave hope to classify rational conformal field theories with arbitrary central charge [3,4]. The W 3 algebra was subsequently studied extensively and a myriad of generalisations were proposed, see [5][6][7][8] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Galilean contractions of W -algebras

Rasmussen

Raymond

2017

Nuclear Physics B

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Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as W -algebras. Known examples include contractions of pairs of the Virasoro algebra, its N = 1 superconformal extension, or the W 3 algebra. Here, we introduce a contraction prescription of the corresponding operator-product algebras, or equivalently, a prescription for contracting tensor products of vertex algebras. With this, we work out the Galilean conformal algebras arising from contractions of N = 2 and N = 4 superconformal algebras as well as of the W -algebras W (2, 4), W (2, 6), W 4 , and W 5 . The latter results provide evidence for the existence of a whole new class of W -algebras which we call Galilean W -algebras. We also apply the contraction prescription to affine Lie algebras and find that the ensuing Galilean affine algebras admit a Sugawara construction. The corresponding central charge is level-independent and given by twice the dimension of the underlying finite-dimensional Lie algebra. Finally, applications of our results to the characterisation of structure constants in W -algebras are proposed.

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“…Всё это указывает на то, что высшие гамильтонианы могут, казалось бы, быть правыми частями некоторых высших аналогов уравнений Книжника-Замо-лодчикова. Однако получить такие уравнения оказывается невозможным, так как невозможно представить действие гамильтонианов Годена через дифференциальные операторы [13], [14].…”

Section: 12unclassified

$W$-Алгебры И Высшие Аналоги Уравнения Книжника - Замолодчикова

Артамонов¹,

Golubeva²

2015

ТМФ

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W-algebras and their representations

Cited by 12 publications

References 48 publications

Topologically massive higher spin gravity

Topologically massive higher spin gravity

Galilean contractions of W -algebras

$W$-Алгебры И Высшие Аналоги Уравнения Книжника - Замолодчикова

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