We study the mechanism of topological mass-generation for 3d Chern-Simons (CS) gauge theories, where the CS term can retain the gauge symmetry and make gauge boson topologically massive. Without CS term the 3d massless gauge boson has a single physical transverse polarization state, while adding the CS term converts it into a massive physical polarization state and conserves the total physical degrees of freedom. We formulate the mechanism of topological mass-generation at S-matrix level. For this, we propose and prove a Topological Equivalence Theorem (TET) which connects the N-point scattering amplitude of the gauge boson’s physical polarization states ( $$ {A}_{\mathrm{P}}^a $$ ) to that of the transverse polarization states ( $$ {A}_{\mathrm{T}}^a $$ ) under high energy expansion. We present a general 3d power counting method on the leading energy dependence of the scattering amplitudes in both topologically massive Yang-Mills (TMYM) and topologically massive gravity (TMG) theories. With these, we uncover a general energy cancellation mechanism for N -gauge boson scattering amplitudes which predicts the cancellation E 4 → E 4−N at tree level. Then, we compute the 4-gauge boson amplitudes of $$ {A}_{\mathrm{P}}^a $$ -states and $$ {A}_{\mathrm{T}}^a $$ -states, with which we explicitly demonstrate the TET and establish such energy cancellations for N = 4. We further extend the double-copy approach to reconstruct the massive 4-graviton amplitude of TMG from the massive 4-gauge boson amplitude of TMYM. With these, we uncover striking large energy cancellations in the 4-graviton amplitude: E 12 → E 1, and establish its correspondence to the leading energy cancellation E 4 → E 0 in the 4-gauge boson amplitude of TMYM.
{ "_oai": { "updated": "2022-05-18T15:13:01Z", "id": "oai:repo.scoap3.org:67854", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "China", "value": "Tsung-Dao Lee Institute & School of Physics and Astronomy, Key Laboratory for Particle Astrophysics and Cosmology (MOE), Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai, 200240, China", "organization": "Shanghai Jiao Tong University" } ], "surname": "Hang", "email": "yfhang@sjtu.edu.cn", "full_name": "Hang, Yan-Feng", "given_names": "Yan-Feng" }, { "affiliations": [ { "country": "China", "value": "Tsung-Dao Lee Institute & School of Physics and Astronomy, Key Laboratory for Particle Astrophysics and Cosmology (MOE), Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai, 200240, China", "organization": "Shanghai Jiao Tong University" }, { "country": "China", "value": "Institute of Modern Physics and Department of Physics, Tsinghua University, Beijing, 100084, China", "organization": "Institute of Modern Physics and Department of Physics, Tsinghua University" }, { "country": "China", "value": "Center for High Energy Physics, Peking University, Beijing, 100871, China", "organization": "Center for High Energy Physics, Peking University" } ], "surname": "He", "email": "hjhe@sjtu.edu.cn", "full_name": "He, Hong-Jian", "given_names": "Hong-Jian" }, { "affiliations": [ { "country": "China", "value": "Tsung-Dao Lee Institute & School of Physics and Astronomy, Key Laboratory for Particle Astrophysics and Cosmology (MOE), Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai, 200240, China", "organization": "Shanghai Jiao Tong University" } ], "surname": "Shen", "email": "cong.shen@epfl.ch", "full_name": "Shen, Cong", "given_names": "Cong" } ], "titles": [ { "source": "Springer", "title": "Structure of Chern-Simons scattering amplitudes from topological equivalence theorem and double-copy" } ], "dois": [ { "value": "10.1007/JHEP01(2022)153" } ], "publication_info": [ { "page_end": "43", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2022", "artid": "JHEP01(2022)153", "year": 2022, "page_start": "1", "journal_issue": "1" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2022-05-18T15:07:07.953606", "source": "Springer", "method": "Springer", "submission_number": "fc976102d6bb11eca1a1661ec451a4e4" }, "page_nr": [ 43 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2022" } ], "control_number": "67854", "record_creation_date": "2022-01-28T15:30:24.577858", "_files": [ { "checksum": "md5:7a192e4e5fa07ba6799fb760fe455c3a", "filetype": "xml", "bucket": "f8488dc6-377e-410c-9b64-4273d1d5c112", "version_id": "1369d197-cb2c-4ca2-b1a6-262a8512a2d0", "key": "10.1007/JHEP01(2022)153.xml", "size": 16431 }, { "checksum": "md5:46dbeaffb2fd24575b236671f0ca6164", "filetype": "pdf/a", "bucket": "f8488dc6-377e-410c-9b64-4273d1d5c112", "version_id": "e7a729da-2002-44f9-8d4c-a6e52f0ff659", "key": "10.1007/JHEP01(2022)153_a.pdf", "size": 762670 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "gr-qc", "hep-ph" ], "value": "2110.05399" } ], "abstracts": [ { "source": "Springer", "value": "We study the mechanism of topological mass-generation for 3d Chern-Simons (CS) gauge theories, where the CS term can retain the gauge symmetry and make gauge boson topologically massive. Without CS term the 3d massless gauge boson has a single physical transverse polarization state, while adding the CS term converts it into a massive physical polarization state and conserves the total physical degrees of freedom. We formulate the mechanism of topological mass-generation at S-matrix level. For this, we propose and prove a Topological Equivalence Theorem (TET) which connects the N-point scattering amplitude of the gauge boson\u2019s physical polarization states ( <math> <msubsup> <mi>A</mi> <mi>P</mi> <mi>a</mi> </msubsup> </math> $$ {A}_{\\mathrm{P}}^a $$ ) to that of the transverse polarization states ( <math> <msubsup> <mi>A</mi> <mi>T</mi> <mi>a</mi> </msubsup> </math> $$ {A}_{\\mathrm{T}}^a $$ ) under high energy expansion. We present a general 3d power counting method on the leading energy dependence of the scattering amplitudes in both topologically massive Yang-Mills (TMYM) and topologically massive gravity (TMG) theories. With these, we uncover a general energy cancellation mechanism for N -gauge boson scattering amplitudes which predicts the cancellation E 4 \u2192 E 4\u2212N at tree level. Then, we compute the 4-gauge boson amplitudes of <math> <msubsup> <mi>A</mi> <mi>P</mi> <mi>a</mi> </msubsup> </math> $$ {A}_{\\mathrm{P}}^a $$ -states and <math> <msubsup> <mi>A</mi> <mi>T</mi> <mi>a</mi> </msubsup> </math> $$ {A}_{\\mathrm{T}}^a $$ -states, with which we explicitly demonstrate the TET and establish such energy cancellations for N = 4. We further extend the double-copy approach to reconstruct the massive 4-graviton amplitude of TMG from the massive 4-gauge boson amplitude of TMYM. With these, we uncover striking large energy cancellations in the 4-graviton amplitude: E 12 \u2192 E 1, and establish its correspondence to the leading energy cancellation E 4 \u2192 E 0 in the 4-gauge boson amplitude of TMYM." } ], "imprints": [ { "date": "2022-01-26", "publisher": "Springer" } ] }