@article{ae56926885374dfa9edb3f835488ebff,
title = "Mass hierarchies in supersymmetric theories",
abstract = "It is argued that large gauge hierarchies occur naturally in some theories with supersymmetry spontaneously broken at the three level. Such theories may also lead to time-dependent values of the natural {"}constants{"}.",
author = "Edward Witten",
note = "Funding Information: Since we assume a simple gauge group, the Fayet-Iliopoulos D term \textbackslash{}[associated with elementary U(1) gauge fields\textbackslash{}] is not available as a mechanism for symmetry breaking. Supersymmetry breaking must be obtained as a variant of the O'Raifeartaigh model \textbackslash{}[7\textbackslash{}]. In this model, there are three complex fields,A, X and Y, and the superspace potential is W(A, X, Y) = XX(A 2 -M 2) + gYA * 2. The potential energy of the scalar fields is V = 2\textasciitilde{} I\textasciitilde{}W/O\textasciitilde{}il2 or in this case 1 Permanent address: Joseph Henry Laboratories, Princeton University, Princeton, NJ 08540, USA. Supported in part by NSF Grant PHYS0-19754. ,1 For previous discussions of the hierarchy problem based on supersymmetry, see refs. \textbackslash{}[4-6\textbackslash{}]. ,2 All models in this paper are natural in the strong sense that the most general W compatible with certain symmetries is used. Since W undergoes no renormalization in perturba-tion theory \textbackslash{}[8,6\textbackslash{}]a weaker concept of naturalness - all terms in W should have coefficients of the same order of magnitude - may be physieaUy adequate. The relevant global symmetries of the O'Raffeaxtaigh model axe Y --* -Y,A --, -A and also X--, el\textasciitilde{}X, Y-+ elay. (Recall that any transformation in which W changes only by an overall phase is a symmetry of a supersymmetric model.)",
year = "1981",
month = oct,
day = "8",
doi = "10.1016/0370-2693(81)90885-6",
language = "English (US)",
volume = "105",
pages = "267--271",
journal = "Physics Letters B",
issn = "0370-2693",
publisher = "Elsevier B.V.",
number = "4",
}