Nonperturbative dynamics of (2+1)d ϕ 4-theory from Hamiltonian truncation
Abstract 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,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2021)190 |
| _version_ | 1818670708496007168 |
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| author | Nikhil Anand Emanuel Katz Zuhair U. Khandker Matthew T. Walters |
| author_facet | Nikhil Anand Emanuel Katz Zuhair U. Khandker Matthew T. Walters |
| author_sort | Nikhil Anand |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-17T07:12:24Z |
| format | Article |
| id | doaj.art-f8dd457a6dc946e8a8d355266cc3c1e1 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-17T07:12:24Z |
| publishDate | 2021-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f8dd457a6dc946e8a8d355266cc3c1e12022-12-21T21:59:01ZengSpringerOpenJournal of High Energy Physics1029-84792021-05-012021517510.1007/JHEP05(2021)190Nonperturbative dynamics of (2+1)d ϕ 4-theory from Hamiltonian truncationNikhil Anand0Emanuel Katz1Zuhair U. Khandker2Matthew T. Walters3Department of Physics, McGill UniversityDepartment of Physics, Boston UniversityDepartment of Physics, Boston UniversityTheoretical Physics Department, CERNAbstract 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.https://doi.org/10.1007/JHEP05(2021)190Conformal Field TheoryNonperturbative EffectsRenormalization GroupField Theories in Lower Dimensions |
| spellingShingle | Nikhil Anand Emanuel Katz Zuhair U. Khandker Matthew T. Walters Nonperturbative dynamics of (2+1)d ϕ 4-theory from Hamiltonian truncation Journal of High Energy Physics Conformal Field Theory Nonperturbative Effects Renormalization Group Field Theories in Lower Dimensions |
| title | Nonperturbative dynamics of (2+1)d ϕ 4-theory from Hamiltonian truncation |
| title_full | Nonperturbative dynamics of (2+1)d ϕ 4-theory from Hamiltonian truncation |
| title_fullStr | Nonperturbative dynamics of (2+1)d ϕ 4-theory from Hamiltonian truncation |
| title_full_unstemmed | Nonperturbative dynamics of (2+1)d ϕ 4-theory from Hamiltonian truncation |
| title_short | Nonperturbative dynamics of (2+1)d ϕ 4-theory from Hamiltonian truncation |
| title_sort | nonperturbative dynamics of 2 1 d ϕ 4 theory from hamiltonian truncation |
| topic | Conformal Field Theory Nonperturbative Effects Renormalization Group Field Theories in Lower Dimensions |
| url | https://doi.org/10.1007/JHEP05(2021)190 |
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