Free-field realisations of the BMS${}_3$ algebra and its extensions

Abstract

We construct an explicit realisation of the BMS${}_3$ algebra with nonzero central charges using holomorphic free fields. This can be extended by the addition of chiral matter to a realisation having arbitrary values for the two independent central charges. Via the introduction of additional free fields, we extend our construction to the minimally supersymmetric BMS${}_3$ algebra and to the nonlinear higher-spin BMS${}_3$-W${}_3$ algebra. We also describe an extended system that realises both the SU(2) current algebra as well as BMS${}_3$ via the Wakimoto representation, though in this case introducing a central extension also brings in new non-central operators.

1+18 pages, expanded version, new section on higher-spin BMS${}_3$-W${}_3$ added, JHEP Version

References in corpus (6)

• The BMS/GCA correspondence
• Asymptotic symmetries and dynamics of three-dimensional flat supergravity
• BMS Modules in Three Dimensions
• 3D Flat Holography: Entropy and Logarithmic Corrections
• Unitarity in three-dimensional flat space higher spin theories
• Lambda: A Mathematica-package for operator product expansions in vertex algebras

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• N=4 Supersymmetric BMS3 algebras from asymptotic symmetry analysis
• Integrable systems with BMS${}_3$ Poisson structure and the dynamics of locally flat spacetimes
• The complex null string, Galilean conformal algebra and scattering equations
• Maximally $\mathcal{N}$-extended super-BMS${}_3$ algebras and Generalized 3D Gravity Solutions
• On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions
• New N=2 SuperBMS${}_3$ algebra and Invariant Dual Theory for 3D Supergravity
• Asymptotic symmetries in spatially flat FRW
• Extended Supersymmetric BMS${}_3$ algebras and Their Free Field Realisations
• Self-dual and logarithmic representations of the twisted Heisenberg--Virasoro algebra at level zero
• Asymptotic Symmetry of Four Dimensional Einstein-Yang-Mills and Einstein-Maxwell Theory
• Equivalent Dual Theories for 3D N=2 Supergravity
• The BRST quantisation of chiral BMS-like field theories
• Dual Theory for maximally $\mathcal{N}$ extended flat Supergravity
• Remarks on BMS${}_3$ invariant field theories: correlation functions and nonunitary CFTs
• Galilean $W_3$ algebra
• Free-field construction of Carrollian $W_N$-algebras