23 July 1982 | R. Barbieri, S. Ferrara, C.A. Savoy
The paper presents a framework for gauge theories with spontaneously broken local supersymmetry, where supersymmetry breaking is induced by gravitational effects. The effective low-energy Lagrangian is derived from the coupling of Yang-Mills matter systems to n=1 supergravity. The model includes realistic examples of supersymmetric QED and electroweak theories with supersymmetry breaking induced by gravitational interactions.
The key idea is that supersymmetry breaking occurs through supergravity couplings, leading to a soft breaking of supersymmetry. This allows for the construction of gauge models with a realistic tree-level mass spectrum. The super-Higgs effect and the Higgs effect coexist, resulting in the generation of gravitino mass. The scalar field z, which acquires a vacuum expectation value (VEV) of order $ M_p $, plays a central role in this process. The scale of supersymmetry breaking is taken to be $ d \simeq \mu M_p $, with $ \mu << M_p $.
The soft breaking of supersymmetry has a universal structure, preserving the ultraviolet properties of globally supersymmetric models and manifesting the mass formulae of spontaneously broken local supersymmetry. The effective low-energy scalar potential is derived, showing that the supergravity scalar potential becomes a pure mass term for the z-field and a globally supersymmetric chiral potential with two soft breaking terms.
The fermion part of the matter Lagrangian is similar to global supersymmetry, with the superpotential $ g(y) $ replaced by $ \widetilde{g}(y) $. The scalar mass matrix and fermion mass matrix are derived, showing that the masses of the scalar partners of leptons and quarks are equal to the gravitino mass up to corrections from Yukawa couplings.
The paper discusses two illustrative examples: a locally supersymmetric extension of QED and an extension of the Glashow-Weinberg-Salam model. In the QED example, the model exhibits spontaneously broken local supersymmetry with a realistic mass spectrum. In the electroweak example, the model predicts realistic electroweak interactions with scalar masses and vector boson masses consistent with experimental data.
The paper concludes that the super-Higgs and normal Higgs effects can coexist if the scale of gauge breaking is at least of the same order as the gravitino mass. The approach can be extended to supersymmetric grand unified theories, and the general feature of supersymmetry breaking induced by supergravity is the existence of a new complex scalar field responsible for the spontaneous breaking of supersymmetry. The model predicts a supersymmetry breaking parameter $ d \simeq 10^{21 \pm 1} \mathrm{GeV}^2 $.The paper presents a framework for gauge theories with spontaneously broken local supersymmetry, where supersymmetry breaking is induced by gravitational effects. The effective low-energy Lagrangian is derived from the coupling of Yang-Mills matter systems to n=1 supergravity. The model includes realistic examples of supersymmetric QED and electroweak theories with supersymmetry breaking induced by gravitational interactions.
The key idea is that supersymmetry breaking occurs through supergravity couplings, leading to a soft breaking of supersymmetry. This allows for the construction of gauge models with a realistic tree-level mass spectrum. The super-Higgs effect and the Higgs effect coexist, resulting in the generation of gravitino mass. The scalar field z, which acquires a vacuum expectation value (VEV) of order $ M_p $, plays a central role in this process. The scale of supersymmetry breaking is taken to be $ d \simeq \mu M_p $, with $ \mu << M_p $.
The soft breaking of supersymmetry has a universal structure, preserving the ultraviolet properties of globally supersymmetric models and manifesting the mass formulae of spontaneously broken local supersymmetry. The effective low-energy scalar potential is derived, showing that the supergravity scalar potential becomes a pure mass term for the z-field and a globally supersymmetric chiral potential with two soft breaking terms.
The fermion part of the matter Lagrangian is similar to global supersymmetry, with the superpotential $ g(y) $ replaced by $ \widetilde{g}(y) $. The scalar mass matrix and fermion mass matrix are derived, showing that the masses of the scalar partners of leptons and quarks are equal to the gravitino mass up to corrections from Yukawa couplings.
The paper discusses two illustrative examples: a locally supersymmetric extension of QED and an extension of the Glashow-Weinberg-Salam model. In the QED example, the model exhibits spontaneously broken local supersymmetry with a realistic mass spectrum. In the electroweak example, the model predicts realistic electroweak interactions with scalar masses and vector boson masses consistent with experimental data.
The paper concludes that the super-Higgs and normal Higgs effects can coexist if the scale of gauge breaking is at least of the same order as the gravitino mass. The approach can be extended to supersymmetric grand unified theories, and the general feature of supersymmetry breaking induced by supergravity is the existence of a new complex scalar field responsible for the spontaneous breaking of supersymmetry. The model predicts a supersymmetry breaking parameter $ d \simeq 10^{21 \pm 1} \mathrm{GeV}^2 $.