Free-field construction of Carrollian $W_N$-algebras

Abstract

We study Carrollian contractions of $W_N$-algebras from a free-field perspective. Using a contraction of the Miura transformation, we obtain explicit free-field realizations of the resulting Carrollian $W_N$-algebras. At the classical level, they are isomorphic to the Galilean $W_N$-algebras. In the quantum case, we distinguish between two Carrollian constructions: a flipped Carrollian contraction, where the time direction is reversed in one sector, and a symmetric contraction. The flipped construction yields a quantum algebra isomorphic to the Galilean one, whereas the symmetric construction produces a distinct quantum Carrollian $W_N$-algebra whose basic structure constants are identical to those of the classical Carrollian $W_N$-algebra. These algebras provide a natural framework for studying extended symmetries in Carrollian conformal field theories, motivated by recent developments in flat space holography. Our construction provides tools for developing the representation theory of Carrollian (and Galilean) $W_N$-algebras using free-field techniques.

28 pages, 1 figure

References in corpus (22)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• The BMS/GCA correspondence
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Carrollian Perspective on Celestial Holography
• Flat Holography: Aspects of the dual field theory
• Fractons, dipole symmetries and curved spacetime
• Magic Fermions: Carroll and Flat Bands
• Conformal Carroll Scalars with Boosts
• Super-BMS${}_3$ algebras from $\mathcal{N}=2$ flat supergravities
• Supersymmetric Extension of Galilean Conformal Algebras
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• Carrollian Origins of Bjorken Flow
• Carroll black holes
• Holographic Lorentz and Carroll Frames
• Boundary dynamics of asymptotically flat 3D gravity coupled to higher spin fields
• Unitarity in three-dimensional flat space higher spin theories
• Integrable systems and the boundary dynamics of higher spin gravity on AdS${}_3$
• Higher-spin gauge theories in three spacetime dimensions
• Chern-Simons action and the Carrollian Cotton tensors
• Galilean $W_3$ algebra