Comment on the cosmological constant for $λϕ^4$ theory in $d$ spacetime dimensions
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arXiv
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| Natura: | Preprint |
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2023
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| _version_ | 1866914032700620800 |
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| author | LeClair, André |
| author_facet | LeClair, André |
| contents | In a recent article we showed that the analog of the cosmological constant in two spacetime dimensions for a wide variety of integrable quantum field theories has the form $ρ_{\rm vac} = - m^2 /2 \mathfrak{g} $ where $m$ is a physical mass and $\mathfrak{g} $ is a generalized coupling, where in the free field limit $\mathfrak{g} \to 0$, $ρ_{\rm vac}$ diverges. We speculated that in four spacetime dimensions $ρ_{\rm vac} $ takes a similar form $ρ_{\rm vac} = - m^4/2 \mathfrak{g}$, but did not support this idea in any specific model. In this article we study this problem for $λϕ^4$ theory in $d$ spacetime dimensions. We show how to obtain the exact $ρ_{\rm vac}$ for the sinh-Gordon theory in the weak coupling limit by using a saddle point approximation. This calculation indicates that the cosmological constant can be well-defined, positive or negative, without spontaneous symmetry breaking. We also show that $ρ_{\rm vac}$ satisfies a Callan-Symanzik type of renormalization group equation. For the most interesting case physically, $ρ_{\rm vac}$ is positive and can arise from a marginally relevant negative coupling $\mathfrak{g}$ and the cosmological constant flows to zero at low energies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13075 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Comment on the cosmological constant for $λϕ^4$ theory in $d$ spacetime dimensions LeClair, André High Energy Physics - Theory General Relativity and Quantum Cosmology In a recent article we showed that the analog of the cosmological constant in two spacetime dimensions for a wide variety of integrable quantum field theories has the form $ρ_{\rm vac} = - m^2 /2 \mathfrak{g} $ where $m$ is a physical mass and $\mathfrak{g} $ is a generalized coupling, where in the free field limit $\mathfrak{g} \to 0$, $ρ_{\rm vac}$ diverges. We speculated that in four spacetime dimensions $ρ_{\rm vac} $ takes a similar form $ρ_{\rm vac} = - m^4/2 \mathfrak{g}$, but did not support this idea in any specific model. In this article we study this problem for $λϕ^4$ theory in $d$ spacetime dimensions. We show how to obtain the exact $ρ_{\rm vac}$ for the sinh-Gordon theory in the weak coupling limit by using a saddle point approximation. This calculation indicates that the cosmological constant can be well-defined, positive or negative, without spontaneous symmetry breaking. We also show that $ρ_{\rm vac}$ satisfies a Callan-Symanzik type of renormalization group equation. For the most interesting case physically, $ρ_{\rm vac}$ is positive and can arise from a marginally relevant negative coupling $\mathfrak{g}$ and the cosmological constant flows to zero at low energies. |
| title | Comment on the cosmological constant for $λϕ^4$ theory in $d$ spacetime dimensions |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2304.13075 |