On Free Field Realizations of W(2,2)-Modules

Adamović, Dražen; Radobolja, Gordan

doi:10.3842/sigma.2016.113

Cited by 8 publications

(17 citation statements)

References 18 publications

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“…Other avenues for future research include representation theory and free-field realisations. The representation theory of the Galilean Virasoro algebra, also known as the W (2, 2) algebra, has already been studied in some detail [46,47,48,49,50,51]. In general, though, the representation theory of Galilean algebras remains largely undeveloped and is entirely unexplored in the case of the higher-order algebras introduced in the present note.…”

Section: Discussionmentioning

confidence: 95%

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Higher-order Galilean contractions

Rasmussen

Raymond

2019

Nuclear Physics B

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A Galilean contraction is a way to construct Galilean conformal algebras from a pair of infinitedimensional conformal algebras, or equivalently, a method for contracting tensor products of vertex algebras. Here, we present a generalisation of the Galilean contraction prescription to allow for inputs of any finite number of conformal algebras, resulting in new classes of higher-order Galilean conformal algebras. We provide several detailed examples, including infinite hierarchies of higher-order Galilean Virasoro algebras, affine Kac-Moody algebras and the associated Sugawara constructions, and W 3 algebras.

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Section: Discussionmentioning

confidence: 95%

“…This includes the representation theory of the Galilean algebras alluded to above. Although realisations of the Galilean Virasoro algebra and some of its superconformal extensions have been considered [61,51,45], a systematic approach and general results are still lacking.…”

Section: Discussionmentioning

confidence: 99%

Higher-order Galilean contractions

Rasmussen

Raymond

2019

Nuclear Physics B

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“…In this section, we review the isomorphism between the BMS 3 and the W(2,2) algebras [35][36][37]51]. We mainly follow the notation of [43], but [32,[39][40][41][42][43][44][45][46][47] may be useful.…”

Section: Bms(3) As a Chiral W(22) Algebramentioning

confidence: 99%

“…The Verma module for the W (2, 2) algebra has been constructed in [35][36][37] . Furthermore, the algebras (1.2) and (2.10) are clearly isomorphic; therefore, we make the following identifications: c M ≡ c 2 and W (z) ≡ M (z).…”

Section: Bms(3) As a Chiral W(22) Algebramentioning

confidence: 99%

“…We try to remedy this situation using a third realization of the BMS 3 algebra: it has been shown that it is also isomorphic to the W (2, 2) algebra [31,[33][34][35][36][37], and that is the viewpoint we adopt in the present work. Roughly speaking, the W (2, 2) algebra is a W algebra defined by the stress-energy tensor and an additional spin-2 field W (z).…”

Section: Introductionmentioning

confidence: 99%

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Remarks on BMS3 invariant field theories: Correlation functions and nonunitary CFTs

Araujo

2018

Phys. Rev. D

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We use the isomorphism between the BMS 3 and the Wð2; 2Þ algebras to reconsider some generic aspects of conformal field theories (CFTs) with the BMS 3 algebra defined as a chiral symmetry. For unitarity theories, it is known that the extended symmetry generator acts trivially, and the resulting theory is equivalent to a CFT with a Virasoro symmetry only. For nonunitary CFTs, we define an operator depending on a nilpotent variable, and we organize the Verma module through the action of this new operator. Finally, we find the conditions imposed by the modified Ward identity.

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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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On Free Field Realizations of W(2,2)-Modules

Cited by 8 publications

References 18 publications

Higher-order Galilean contractions

Higher-order Galilean contractions

Remarks on BMS3 invariant field theories: Correlation functions and nonunitary CFTs

Galilean contractions of W -algebras

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