2013/05/22 by Jan Holland, Stefan Hollands · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmological constant #Cosmology and Gravitation Theories #Coupling constant #Extrapolation #Mathematical analysis #Mathematical physics #Minkowski space #Noncommutative and Quantum Gravity Theories #Operator (biology) #Perturbation theory (quantum mechanics) #Physics #Quantum mechanics #Theoretical physics #Vacuum energy #Vacuum polarization #Vacuum state #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/31/12/125006
published as Class. Quantum Grav. 31 (2014) 125006 · 11 pages
arxiv created 2013/05/22 · openalex publication_date 2014/05/27 · arxiv updated 2014/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We propose an explanation for the ‘unnatural smallness’ of the cosmological constant, arguing that the stress–energy tensor of the Standard Model should be given by 〈 T μν 〉 = ρ vac η μν , with a vacuum energy ρ vac that differs from the usual ‘dimensional analysis’ result by an exponentially small factor associated with non-perturbative effects. We substantiate our proposal by a rigorous analysis of a toy model, namely the two-dimensional Gross–Neveu model. The stress energy operator is constructed concretely via the operator-product-expansion, and the inherent ambiguities in its construction are carefully examined. Our result for the vacuum energy is then obtained from the assumptions that (a) the OPE-coefficients have an analytic dependence on g , which we propose to be a generic feature of QFT, and that (b) the vacuum energy vanishes to all orders in perturbation theory. Our result can also be interpreted as saying that, while the semi-classical Einstein’s equation can be fulfilled in Minkowski space at the perturbative level, it cannot at the non-perturbative level. Extrapolating our result from the Gross–Neveu model to the Standard Model, one would expect to find , where Λ is an energy scale such as Λ = M H , and g is a gauge coupling such as g 2 /4π = α EW . Assuming this extrapolation is justified, the exponentially small factor due to non-perturbative effects would explain why this quantity is tiny, instead of strictly zero.