Version 1
: Received: 19 May 2023 / Approved: 22 May 2023 / Online: 22 May 2023 (10:47:41 CEST)
How to cite:
Leclair, A. Comment on the Cosmological Constant for λϕ4 Theory in D Spacetime Dimensions. Preprints2023, 2023051506. https://doi.org/10.20944/preprints202305.1506.v1
Leclair, A. Comment on the Cosmological Constant for λϕ4 Theory in D Spacetime Dimensions. Preprints 2023, 2023051506. https://doi.org/10.20944/preprints202305.1506.v1
Leclair, A. Comment on the Cosmological Constant for λϕ4 Theory in D Spacetime Dimensions. Preprints2023, 2023051506. https://doi.org/10.20944/preprints202305.1506.v1
APA Style
Leclair, A. (2023). Comment on the Cosmological Constant for λϕ4 Theory in D Spacetime Dimensions. Preprints. https://doi.org/10.20944/preprints202305.1506.v1
Chicago/Turabian Style
Leclair, A. 2023 "Comment on the Cosmological Constant for λϕ4 Theory in D Spacetime Dimensions" Preprints. https://doi.org/10.20944/preprints202305.1506.v1
Abstract
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 ρvac = −m2/2g where m is a physical mass and g is a generalized coupling, where in the free field limit g → 0, ρvac diverges. We speculated that in four spacetime dimensions ρvac takes a similar form ρvac = −m4/2g, but did not support this idea in any specific model. In this article we study this problem for λφ4theory in d spacetime dimensions. We show how to obtain the exact ρvac 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 ρvac satisfies a Callan-Symanzik type of renormalization group equation. For the most interesting case physically, ρvac is positive and can arise from a marginally relevant negative coupling g and the cosmological constant flows to zero at low energies.
Keywords
cosmological constant; quantum field theory
Subject
Physical Sciences, Theoretical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
