Non-Lorentzian Kač-Moody Algebras

Abstract

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 $c\to \infty$) and Carrollian ($c\to 0$) 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.

arXiv comment56 pages

References in corpus (31)

• The BMS/GCA correspondence
• Conformal Carroll groups and BMS symmetry
• Galilean Conformal Algebras and AdS/CFT
• A New Cosmological Scenario in String Theory
• Holography of 3d Flat Cosmological Horizons
• The flat limit of three dimensional asymptotically anti-de Sitter spacetimes
• Carrollian Perspective on Celestial Holography
• Flat Holography: Aspects of the dual field theory
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Entanglement entropy in Galilean conformal field theories and flat holography
• GCA in 2d
• Classical and Quantized Tensionless Strings
• Tensionless String Spectra on ${\mathrm{AdS}}_3$
• Entanglement Entropy in Flat Holography
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Tensionless Strings and Galilean Conformal Algebra
• On Representations and Correlation Functions of Galilean Conformal Algebras
• Tensionless Strings from Worldsheet Symmetries
• Holographic Reconstruction of 3D Flat Space-Time
• Tensionless Strings, WZW Models at Critical Level and Massless Higher Spin Fields
• MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere
• Stress tensor correlators in three-dimensional gravity
• A Tale of Three. Tensionless strings and vacuum structure
• A BMS-invariant free scalar model
• Charged structure constants from modularity
• Generalizing the ${\mathfrak{bms}}_3$ and 2D-conformal algebras by expanding the Virasoro algebra
• Intrinsic Approach to $1+1$D Carrollian Conformal Field Theory
• Spectral Flow in 3D Flat Spacetimes
• Higher-order Galilean contractions
• Multi-graded Galilean conformal algebras

Cited by in corpus (3)

• Carrollian Approach to $1+3$D Flat Holography
• Symmetry Resolution in non-Lorentzian Field Theories
• Irrelevant and marginal deformed BMS field theories