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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Format: | Article |
Language: | English |
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SpringerOpen
2022-12-01
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Series: | Journal of High Energy Physics |
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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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institution | Directory Open Access Journal |
issn | 1029-8479 |
language | English |
last_indexed | 2024-04-09T21:39:46Z |
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series | Journal of High Energy Physics |
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 |