Higher-order Galilean contractions

Rasmussen, Jørgen; Raymond, Christopher

doi:10.1016/j.nuclphysb.2019.114680

Cited by 5 publications

(7 citation statements)

References 90 publications

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“…Although our presentation focuses on the case of two input algebras, the generalisation to any number of input algebras is straightforward. Such algebras have higher-order Galilean subalgebras [35] with OPEs between the fields in G n ℓ ℓ determined by Proposition 3.1. Our asymmetric Galilean contraction procedure provides a unifying framework for several interesting examples in the CFT literature, from early work on non-compact WZW models to current work on tensionless strings and super-BMS symmetries.…”

Section: Discussionmentioning

confidence: 99%

“…For n = 0, the contraction results in a well-defined algebra with two conformal-weight 2 quasiprimary fields. This is a novel Galilean structure that cannot be realised using higher-order, or multi-graded, Galilean contractions [35,21].…”

Section: The Asymmetric Galilean Virasoro Algebramentioning

confidence: 99%

“…The Galilean contraction procedure has been generalised to allow for the input of any number of symmetry algebras, leading to so-called higher-order Galilean contractions [24,35]. The ensuing Galilean algebras exhibit graded structures of any integer order N 2.…”

Section: Introductionmentioning

confidence: 99%

“…A method to perform Galilean contractions of W -algebras was developed in [31,32,35], and many concrete examples of Galilean W -algebras have been constructed.…”

mentioning

confidence: 99%

“…The Galilean Virasoro subalgebra is generated by T 0 , T 1 , and the fields W ℓ , U 1 are primary with respect to the Virasoro field T 0 . The remaining OPEs are determined by applying the techniques detailed in [32,35].…”

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confidence: 99%

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Multi-graded Galilean conformal algebras

2020

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The usual Galilean contraction procedure for generating new conformal symmetry algebras takes as input a number of symmetry algebras which are equivalent up to central charge. We demonstrate that the equivalence condition can be relaxed by inhomogeneously contracting the chiral algebras and present general results for the ensuing asymmetric Galilean algebras. Several examples relevant to conformal field theory are discussed in detail, including superconformal algebras and W-algebras. We also discuss how the Sugawara construction is modified in the asymmetric setting.

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Section: Discussionmentioning

confidence: 99%

Section: The Asymmetric Galilean Virasoro Algebramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…A method to perform Galilean contractions of W -algebras was developed in [31,32,35], and many concrete examples of Galilean W -algebras have been constructed.…”

mentioning

confidence: 99%

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confidence: 99%

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Multi-graded Galilean conformal algebras

2020

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Non-Lorentzian Kač-Moody algebras

Bagchi

Ritankar

Kaushik

et al. 2023

J. High Energ. Phys.

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We investigate two dimensional (2d) quantum field theories which exhibit Non-Lorentzian Kač-Moody (NLKM) algebras as their underlying symmetry. Our investigations encompass both 2d Galilean (speed of light c → ∞) and Carrollian (c → 0) CFTs with additional number of infinite non-Abelian currents, stemming from an isomorphism between the two algebras. We alternate between an intrinsic and a limiting analysis. Our NLKM algebra is constructed first through a contraction and then derived from an intrinsically Carrollian perspective. We then go on to use the symmetries to derive a Non-Lorentzian (NL) Sugawara construction and ultimately write down the NL equivalent of the Knizhnik Zamolodchikov equations. All of these are also derived from contractions, thus providing a robust cross-check of our analyses.

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