Intrinsic approach to 1 + 1D Carrollian Conformal Field Theory

Abstract The 3D Bondi-Metzner-Sachs (BMS3) algebra that is the asymptotic symmetry algebra at null infinity of the 1 + 2D asymptotically flat space-time is isomorphic to the 1 + 1D Carrollian conformal algebra. Building on this connection, various preexisting results in the BMS3-invariant field theo...

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Main Author: Amartya Saha
Format: Article
Language:English
Published: SpringerOpen 2022-12-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP12(2022)133
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author Amartya Saha
author_facet Amartya Saha
author_sort Amartya Saha
collection DOAJ
description Abstract The 3D Bondi-Metzner-Sachs (BMS3) algebra that is the asymptotic symmetry algebra at null infinity of the 1 + 2D asymptotically flat space-time is isomorphic to the 1 + 1D Carrollian conformal algebra. Building on this connection, various preexisting results in the BMS3-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 + 1D 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 iϵ-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 + 1D Carrollian conformal algebra.
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spelling doaj.art-1e235d89a3b0419eb070aca897d5b4992023-03-26T11:04:29ZengSpringerOpenJournal of High Energy Physics1029-84792022-12-0120221215410.1007/JHEP12(2022)133Intrinsic approach to 1 + 1D Carrollian Conformal Field TheoryAmartya Saha0Department of Physics, Indian Institute of Technology KanpurAbstract The 3D Bondi-Metzner-Sachs (BMS3) algebra that is the asymptotic symmetry algebra at null infinity of the 1 + 2D asymptotically flat space-time is isomorphic to the 1 + 1D Carrollian conformal algebra. Building on this connection, various preexisting results in the BMS3-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 + 1D 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 iϵ-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 + 1D Carrollian conformal algebra.https://doi.org/10.1007/JHEP12(2022)133Scale and Conformal SymmetriesSpace-Time SymmetriesField Theories in Lower Dimensions
spellingShingle Amartya Saha
Intrinsic approach to 1 + 1D Carrollian Conformal Field Theory
Journal of High Energy Physics
Scale and Conformal Symmetries
Space-Time Symmetries
Field Theories in Lower Dimensions
title Intrinsic approach to 1 + 1D Carrollian Conformal Field Theory
title_full Intrinsic approach to 1 + 1D Carrollian Conformal Field Theory
title_fullStr Intrinsic approach to 1 + 1D Carrollian Conformal Field Theory
title_full_unstemmed Intrinsic approach to 1 + 1D Carrollian Conformal Field Theory
title_short Intrinsic approach to 1 + 1D Carrollian Conformal Field Theory
title_sort intrinsic approach to 1 1d carrollian conformal field theory
topic Scale and Conformal Symmetries
Space-Time Symmetries
Field Theories in Lower Dimensions
url https://doi.org/10.1007/JHEP12(2022)133
work_keys_str_mv AT amartyasaha intrinsicapproachto11dcarrollianconformalfieldtheory