@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 \[associated with elementary U(1) gauge fields\] is not available as a mechanism for symmetry breaking. Supersymmetry breaking must be obtained as a variant of the O'Raifeartaigh model \[7\]. 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~ I~W/O~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. \[4-6\]. ,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 \[8,6\]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~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",
number = "4",
}