Mingling of the infrared and ultraviolet and the “cosmological constant” for interacting QFT in 2d
Abstract We propose a proper definition of the vacuum expectation value of the stress energy tensor 〈0| T μν | 0〉 for integrable quantum field theories in two spacetime dimensions, which is the analog of the cosmological constant in 4d. For a wide variety of models, massive or massless, we show ρ va...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2023)222 |
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| author | André LeClair |
| author_facet | André LeClair |
| author_sort | André LeClair |
| collection | DOAJ |
| description | Abstract We propose a proper definition of the vacuum expectation value of the stress energy tensor 〈0| T μν | 0〉 for integrable quantum field theories in two spacetime dimensions, which is the analog of the cosmological constant in 4d. For a wide variety of models, massive or massless, we show ρ vac = − m 2 / 2 g $$ {\rho}_{\textrm{vac}}=-{m}^2/2\mathfrak{g} $$ exactly, where g $$ \mathfrak{g} $$ is a generalized coupling which we compute and m is a basic mass scale. The kinds of models we consider are the massive sinh-Gordon and sine-Gordon theories and perturbations of the Yang-Lee and 3-state Potts models, pure T T ¯ $$ T\overline{T} $$ perturbations of infra-red QFT’s, and UV completions of the latter which are massless flows between UV and IR fixed points. In the massive case m is the physical mass of the lightest particle and g $$ \mathfrak{g} $$ is related to parameters in the 2-body S-matrix. In some examples ρ vac = 0 due to a fractional supersymmetry. For massless cases, m can be a scale of spontaneous symmetry breaking. The “cosmological constant problem” generically arises in the free field limit g $$ \mathfrak{g} $$ → 0, thus interactions can potentially resolve the problem at least for most cases considered in this paper. We speculate on extensions of these results to 4 spacetime dimensions and propose ρ vac = m 4 / 2 g $$ {\rho}_{\textrm{vac}}={m}^4/2\mathfrak{g} $$ , however without integrability we cannot yet propose a precise manner in which to calculate g $$ \mathfrak{g} $$ . Nevertheless, based on cosmological data on ρ vac, if g $$ \mathfrak{g} $$ ~ 1 then it is worth pointing out that the lightest mass particle is on the order of experimental values of proposed neutrino masses. |
| first_indexed | 2024-03-12T13:14:45Z |
| format | Article |
| id | doaj.art-a11d0cc4fff04814b87b8e7096821e34 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T13:14:45Z |
| publishDate | 2023-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a11d0cc4fff04814b87b8e7096821e342023-08-27T11:04:55ZengSpringerOpenJournal of High Energy Physics1029-84792023-05-012023511810.1007/JHEP05(2023)222Mingling of the infrared and ultraviolet and the “cosmological constant” for interacting QFT in 2dAndré LeClair0Physics Department, Cornell UniversityAbstract We propose a proper definition of the vacuum expectation value of the stress energy tensor 〈0| T μν | 0〉 for integrable quantum field theories in two spacetime dimensions, which is the analog of the cosmological constant in 4d. For a wide variety of models, massive or massless, we show ρ vac = − m 2 / 2 g $$ {\rho}_{\textrm{vac}}=-{m}^2/2\mathfrak{g} $$ exactly, where g $$ \mathfrak{g} $$ is a generalized coupling which we compute and m is a basic mass scale. The kinds of models we consider are the massive sinh-Gordon and sine-Gordon theories and perturbations of the Yang-Lee and 3-state Potts models, pure T T ¯ $$ T\overline{T} $$ perturbations of infra-red QFT’s, and UV completions of the latter which are massless flows between UV and IR fixed points. In the massive case m is the physical mass of the lightest particle and g $$ \mathfrak{g} $$ is related to parameters in the 2-body S-matrix. In some examples ρ vac = 0 due to a fractional supersymmetry. For massless cases, m can be a scale of spontaneous symmetry breaking. The “cosmological constant problem” generically arises in the free field limit g $$ \mathfrak{g} $$ → 0, thus interactions can potentially resolve the problem at least for most cases considered in this paper. We speculate on extensions of these results to 4 spacetime dimensions and propose ρ vac = m 4 / 2 g $$ {\rho}_{\textrm{vac}}={m}^4/2\mathfrak{g} $$ , however without integrability we cannot yet propose a precise manner in which to calculate g $$ \mathfrak{g} $$ . Nevertheless, based on cosmological data on ρ vac, if g $$ \mathfrak{g} $$ ~ 1 then it is worth pointing out that the lightest mass particle is on the order of experimental values of proposed neutrino masses.https://doi.org/10.1007/JHEP05(2023)222Renormalization and RegularizationRenormalization GroupThermal Field Theory |
| spellingShingle | André LeClair Mingling of the infrared and ultraviolet and the “cosmological constant” for interacting QFT in 2d Journal of High Energy Physics Renormalization and Regularization Renormalization Group Thermal Field Theory |
| title | Mingling of the infrared and ultraviolet and the “cosmological constant” for interacting QFT in 2d |
| title_full | Mingling of the infrared and ultraviolet and the “cosmological constant” for interacting QFT in 2d |
| title_fullStr | Mingling of the infrared and ultraviolet and the “cosmological constant” for interacting QFT in 2d |
| title_full_unstemmed | Mingling of the infrared and ultraviolet and the “cosmological constant” for interacting QFT in 2d |
| title_short | Mingling of the infrared and ultraviolet and the “cosmological constant” for interacting QFT in 2d |
| title_sort | mingling of the infrared and ultraviolet and the cosmological constant for interacting qft in 2d |
| topic | Renormalization and Regularization Renormalization Group Thermal Field Theory |
| url | https://doi.org/10.1007/JHEP05(2023)222 |
| work_keys_str_mv | AT andreleclair minglingoftheinfraredandultravioletandthecosmologicalconstantforinteractingqftin2d |