We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators 𝒪 in ϕ 4 theory in two dimensions. We show how to use the Hamiltonian eigenstates from LCT to obtain form factors that are matrix elements of a local operator 𝒪 between single-particle bra and ket states, and we develop methods that significantly reduce errors resulting from the finite truncation of the Hilbert space. We extrapolate these form factors as a function of momentum to the regime where, by crossing symmetry, they are form factors of 𝒪 between the vacuum and a two-particle asymptotic scattering state. We also compute the momentum-space time-ordered two-point functions of local operators in LCT. These converge quickly at momenta away from branch cuts, allowing us to indirectly obtain the time-ordered correlator and the spectral density at the branch cuts. We focus on the case where the local operator 𝒪 is the trace Θ of the stress tensor.
{ "_oai": { "updated": "2023-03-10T21:32:51Z", "id": "oai:repo.scoap3.org:69364", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "USA", "value": "Department of Physics, Boston University, Boston, MA, 02215, USA", "organization": "Boston University" } ], "surname": "Chen", "email": "hbchen@bu.edu", "full_name": "Chen, Hongbin", "given_names": "Hongbin" }, { "affiliations": [ { "country": "USA", "value": "Department of Physics, Boston University, Boston, MA, 02215, USA", "organization": "Boston University" } ], "surname": "Fitzpatrick", "email": "fitzpatr@bu.edu", "full_name": "Fitzpatrick, A.", "given_names": "A." }, { "affiliations": [ { "country": "France", "value": "Philippe Meyer Institute, Physics Department \u00c9cole Normale Sup\u00e9rieure (ENS), Universit\u00e9 PSL24 rue Lhomond, Paris, F-75231, France", "organization": "Philippe Meyer Institute, Physics Department \u00c9cole Normale Sup\u00e9rieure (ENS), Universit\u00e9 PSL24 rue Lhomond" } ], "surname": "Karateev", "email": "d.s.karateev@gmail.com", "full_name": "Karateev, Denis", "given_names": "Denis" } ], "titles": [ { "source": "Springer", "title": "Form factors and spectral densities from Lightcone Conformal Truncation" } ], "dois": [ { "value": "10.1007/JHEP04(2022)109" } ], "publication_info": [ { "page_end": "39", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2022", "artid": "JHEP04(2022)109", "year": 2022, "page_start": "1", "journal_issue": "4" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2023-03-10T21:31:20.060632", "source": "Springer", "method": "Springer", "submission_number": "b6222fd2bf8a11eda920065bd8dc6b20" }, "page_nr": [ 39 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2022" } ], "control_number": "69364", "record_creation_date": "2022-04-21T15:30:25.994947", "_files": [ { "checksum": "md5:2ab4b8f58cf657386f34720aac773f93", "filetype": "xml", "bucket": "cb9d1942-7f9d-44df-a8ee-8ab527b5407d", "version_id": "9c6455ca-6644-4cd9-8a30-46fa5fd5204c", "key": "10.1007/JHEP04(2022)109.xml", "size": 11637 }, { "checksum": "md5:3745a75524eedef0059354efdf5ff894", "filetype": "pdf/a", "bucket": "cb9d1942-7f9d-44df-a8ee-8ab527b5407d", "version_id": "d426ba2d-5667-4b7b-b5d0-925264c19a00", "key": "10.1007/JHEP04(2022)109_a.pdf", "size": 2250037 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "cond-mat.str-el", "hep-lat" ], "value": "2107.10285" } ], "abstracts": [ { "source": "Springer", "value": "We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators \ud835\udcaa in \u03d5 4 theory in two dimensions. We show how to use the Hamiltonian eigenstates from LCT to obtain form factors that are matrix elements of a local operator \ud835\udcaa between single-particle bra and ket states, and we develop methods that significantly reduce errors resulting from the finite truncation of the Hilbert space. We extrapolate these form factors as a function of momentum to the regime where, by crossing symmetry, they are form factors of \ud835\udcaa between the vacuum and a two-particle asymptotic scattering state. We also compute the momentum-space time-ordered two-point functions of local operators in LCT. These converge quickly at momenta away from branch cuts, allowing us to indirectly obtain the time-ordered correlator and the spectral density at the branch cuts. We focus on the case where the local operator \ud835\udcaa is the trace \u0398 of the stress tensor." } ], "imprints": [ { "date": "2022-04-20", "publisher": "Springer" } ] }