We use Lightcone Conformal Truncation (LCT)—a version of Hamiltonian truncation — to study the nonperturbative, real-time dynamics of ϕ 4-theory in 2+1 dimensions. This theory has UV divergences that need to be regulated. We review how, in a Hamiltonian framework with a total energy cutoff, renormalization is necessarily state-dependent, and UV sensitivity cannot be canceled with standard local operator counter-terms. To overcome this problem, we present a prescription for constructing the appropriate state-dependent counterterms for (2+1)d ϕ 4-theory in lightcone quantization. We then use LCT with this counterterm prescription to study ϕ 4-theory, focusing on the ℤ2 symmetry-preserving phase. Specifically, we compute the spectrum as a function of the coupling and demonstrate the closing of the mass gap at a (scheme-dependent) critical coupling. We also compute Lorentz-invariant two-point functions, both at generic strong coupling and near the critical point, where we demonstrate IR universality and the vanishing of the trace of the stress tensor.
{ "_oai": { "updated": "2021-09-03T01:29:18Z", "id": "oai:repo.scoap3.org:62136", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "Canada", "value": "Department of Physics, McGill University, 845 Sherbrooke St W, Montr\u00e9al, QC, H3A 1B2, Canada", "organization": "McGill University" } ], "surname": "Anand", "email": "nikhil.anand@mcgill.ca", "full_name": "Anand, Nikhil", "given_names": "Nikhil" }, { "affiliations": [ { "country": "USA", "value": "Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA, 02215, USA", "organization": "Boston University" } ], "surname": "Katz", "email": "amikatz@bu.edu", "full_name": "Katz, Emanuel", "given_names": "Emanuel" }, { "affiliations": [ { "country": "USA", "value": "Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA, 02215, USA", "organization": "Boston University" } ], "surname": "Khandker", "email": "zuhair.khandker@gmail.com", "full_name": "Khandker, Zuhair", "given_names": "Zuhair" }, { "affiliations": [ { "country": "CERN", "value": "Theoretical Physics Department, CERN, Geneva 23, 1211, Switzerland", "organization": "CERN" }, { "country": "Switzerland", "value": "Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne, CH-1015, Switzerland", "organization": "Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL)" } ], "surname": "Walters", "email": "matthew.walters@epfl.ch", "full_name": "Walters, Matthew", "given_names": "Matthew" } ], "titles": [ { "source": "Springer", "title": "Nonperturbative dynamics of (2+1)d \u03d5 4-theory from Hamiltonian truncation" } ], "dois": [ { "value": "10.1007/JHEP05(2021)190" } ], "publication_info": [ { "page_end": "75", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2021", "artid": "JHEP05(2021)190", "year": 2021, "page_start": "1", "journal_issue": "5" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2021-09-03T00:35:16.388151", "source": "Springer", "method": "Springer", "submission_number": "12b7ad860c4e11ecb53772fd3742099d" }, "page_nr": [ 75 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2021" } ], "control_number": "62136", "record_creation_date": "2021-05-21T03:30:22.467440", "_files": [ { "checksum": "md5:051aced4c15a74c2f6473cccbd87c15c", "filetype": "xml", "bucket": "1da79c1d-4fcd-405e-aa35-77615fc18350", "version_id": "157ce497-85af-4b2f-a97f-c8c8e21f32d3", "key": "10.1007/JHEP05(2021)190.xml", "size": 14025 }, { "checksum": "md5:72d7df7b5f98305d4c64c536aac7fc5e", "filetype": "pdf/a", "bucket": "1da79c1d-4fcd-405e-aa35-77615fc18350", "version_id": "0dcbb27f-e64e-48d2-b8b6-e18d19772752", "key": "10.1007/JHEP05(2021)190_a.pdf", "size": 4912072 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "cond-mat.stat-mech", "cond-mat.str-el", "hep-lat" ], "value": "2010.09730" } ], "abstracts": [ { "source": "Springer", "value": "We use Lightcone Conformal Truncation (LCT)\u2014a version of Hamiltonian truncation \u2014 to study the nonperturbative, real-time dynamics of \u03d5 4-theory in 2+1 dimensions. This theory has UV divergences that need to be regulated. We review how, in a Hamiltonian framework with a total energy cutoff, renormalization is necessarily state-dependent, and UV sensitivity cannot be canceled with standard local operator counter-terms. To overcome this problem, we present a prescription for constructing the appropriate state-dependent counterterms for (2+1)d \u03d5 4-theory in lightcone quantization. We then use LCT with this counterterm prescription to study \u03d5 4-theory, focusing on the \u21242 symmetry-preserving phase. Specifically, we compute the spectrum as a function of the coupling and demonstrate the closing of the mass gap at a (scheme-dependent) critical coupling. We also compute Lorentz-invariant two-point functions, both at generic strong coupling and near the critical point, where we demonstrate IR universality and the vanishing of the trace of the stress tensor." } ], "imprints": [ { "date": "2021-05-20", "publisher": "Springer" } ] }