Intrinsic Approach to $1+1$D Carrollian Conformal Field Theory

Abstract

The 3D Bondi-Metzner-Sachs (BMS${}_3$) algebra that is the asymptotic symmetry algebra at null infinity of the $1+2$D asymptotically flat space-time is isomorphic to the $1+1$D Carrollian conformal algebra. Building on this connection, various preexisting results in the BMS${}_3$-invariant field theories are reconsidered in light of a purely Carrollian perspective in this paper. In direct analogy to the covariant transformation laws of the Lorentzian tensors, the flat Carrollian multiplets are defined and their conformal transformation properties are established. A first-principle derivation of the Ward identities in a $1+1$D Carrollian conformal field theory (CCFT) is presented. This derivation introduces the use of the complex contour-integrals (over the space-variable) that provide a strong analytic handle to CCFT. The temporal step-function factors appearing in these Ward identities enable the translation of the operator product expansions (OPEs) into the language of the operator commutation relations and vice versa, via a contour-integral prescription. Motivated by the properties of these step-functions, the $i\epsilon$-forms of the Ward identities and OPEs are proposed that permit for the hassle-free use of the algebraic properties of the latter. Finally, utilizing the computational techniques developed, it is shown that the modes of the quantum energy-momentum tensor operator generate the centrally extended version of the infinite-dimensional $1+1$D Carrollian conformal algebra.

arXiv commentComments and References added

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Cited by in corpus (12)

• Carrollian Approach to $1+3$D Flat Holography
• Carroll fermions in two dimensions
• A BMS-invariant free fermion model
• Symmetry group at future null infinity II: Vector theory
• Carrollian Yang-Mills Theory
• Symmetry Resolution in non-Lorentzian Field Theories
• Quantization of Carrollian conformal scalar theories
• Extended Kinematical 3D Gravity Theories
• Non-Lorentzian Kač-Moody Algebras
• Irrelevant and marginal deformed BMS field theories
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Character of the highest weight module of BMS algebra realized on codimensional-two boundary