Form factors and spectral densities from Lightcone Conformal Truncation
Abstract 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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2022)109 |
| _version_ | 1827985387757240320 |
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| author | Hongbin Chen A. Liam Fitzpatrick Denis Karateev |
| author_facet | Hongbin Chen A. Liam Fitzpatrick Denis Karateev |
| author_sort | Hongbin Chen |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-04-09T23:14:05Z |
| format | Article |
| id | doaj.art-5ab4a9abfab34ee0bd598c4921bb51ed |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:14:05Z |
| publishDate | 2022-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-5ab4a9abfab34ee0bd598c4921bb51ed2023-03-22T10:11:37ZengSpringerOpenJournal of High Energy Physics1029-84792022-04-012022413910.1007/JHEP04(2022)109Form factors and spectral densities from Lightcone Conformal TruncationHongbin Chen0A. Liam Fitzpatrick1Denis Karateev2Department of Physics, Boston UniversityDepartment of Physics, Boston UniversityPhilippe Meyer Institute, Physics Department École Normale Supérieure (ENS), Université PSL24 rue LhomondAbstract 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.https://doi.org/10.1007/JHEP04(2022)109Conformal Field TheoryNonperturbative EffectsRenormalization Group |
| spellingShingle | Hongbin Chen A. Liam Fitzpatrick Denis Karateev Form factors and spectral densities from Lightcone Conformal Truncation Journal of High Energy Physics Conformal Field Theory Nonperturbative Effects Renormalization Group |
| title | Form factors and spectral densities from Lightcone Conformal Truncation |
| title_full | Form factors and spectral densities from Lightcone Conformal Truncation |
| title_fullStr | Form factors and spectral densities from Lightcone Conformal Truncation |
| title_full_unstemmed | Form factors and spectral densities from Lightcone Conformal Truncation |
| title_short | Form factors and spectral densities from Lightcone Conformal Truncation |
| title_sort | form factors and spectral densities from lightcone conformal truncation |
| topic | Conformal Field Theory Nonperturbative Effects Renormalization Group |
| url | https://doi.org/10.1007/JHEP04(2022)109 |
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