In this paper we explicitly carry out the perturbative renormalization of the $$ T\overline{T} $$ -deformed free massive Dirac fermion in two dimensions up to second order in the coupling constant. This is done by computing the two-to-two S-matrix using the LSZ reduction formula and canceling out the divergences by introducing counterterms. We demonstrate that the renormalized Lagrangian is unambiguously determined by demanding that it gives the correct S-matrix of a $$ T\overline{T} $$ -deformed integrable field theory. Remarkably, the renormalized Lagrangian is qualitatively very different from its classical counterpart.
{ "_oai": { "updated": "2021-12-29T09:31:24Z", "id": "oai:repo.scoap3.org:66887", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "Israel", "value": "The Racah Institute of Physics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Jerusalem, 91904, Israel", "organization": "The Hebrew University of Jerusalem" } ], "surname": "Dey", "email": "anshuman.dey@mail.huji.ac.il", "full_name": "Dey, Anshuman", "given_names": "Anshuman" }, { "affiliations": [ { "country": "Israel", "value": "The Racah Institute of Physics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Jerusalem, 91904, Israel", "organization": "The Hebrew University of Jerusalem" } ], "surname": "Fortinsky", "email": "aryeh.fortinsky@mail.huji.ac.il", "full_name": "Fortinsky, Aryeh", "given_names": "Aryeh" } ], "titles": [ { "source": "Springer", "title": "Perturbative renormalization of the <math> <mi>T</mi> <mover> <mi>T</mi> <mo>\u00af</mo> </mover> </math> $$ \\mathrm{T}\\overline{\\mathrm{T}} $$ -deformed free massive Dirac fermion" } ], "dois": [ { "value": "10.1007/JHEP12(2021)200" } ], "publication_info": [ { "page_end": "62", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2021", "artid": "JHEP12(2021)200", "year": 2021, "page_start": "1", "journal_issue": "12" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2021-12-29T09:30:29.466463", "source": "Springer", "method": "Springer", "submission_number": "e4e6930c688911ecbc4196e84b9c3210" }, "page_nr": [ 62 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2021" } ], "control_number": "66887", "record_creation_date": "2021-12-29T09:30:29.466493", "_files": [ { "checksum": "md5:5df459a0d4fbeae437d14f1cf777013e", "filetype": "xml", "bucket": "cbcf19ad-70df-4f8b-b884-4c8d6757a2d7", "version_id": "f3253e03-6129-417b-bd7c-13b8b30f2168", "key": "10.1007/JHEP12(2021)200.xml", "size": 11786 }, { "checksum": "md5:05627d20b695cee092c97114f4c22fda", "filetype": "pdf/a", "bucket": "cbcf19ad-70df-4f8b-b884-4c8d6757a2d7", "version_id": "74781dbb-cc18-40ba-b2e8-bf5d08d5e7a3", "key": "10.1007/JHEP12(2021)200_a.pdf", "size": 990039 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th" ], "value": "2109.10525" } ], "abstracts": [ { "source": "Springer", "value": "In this paper we explicitly carry out the perturbative renormalization of the <math> <mi>T</mi> <mover> <mi>T</mi> <mo>\u00af</mo> </mover> </math> $$ T\\overline{T} $$ -deformed free massive Dirac fermion in two dimensions up to second order in the coupling constant. This is done by computing the two-to-two S-matrix using the LSZ reduction formula and canceling out the divergences by introducing counterterms. We demonstrate that the renormalized Lagrangian is unambiguously determined by demanding that it gives the correct S-matrix of a <math> <mi>T</mi> <mover> <mi>T</mi> <mo>\u00af</mo> </mover> </math> $$ T\\overline{T} $$ -deformed integrable field theory. Remarkably, the renormalized Lagrangian is qualitatively very different from its classical counterpart." } ], "imprints": [ { "date": "2021-12-28", "publisher": "Springer" } ] }