COMPLEX SPINORS AND UNIFIED THEORIES

COMPLEX SPINORS AND UNIFIED THEORIES

1979 | Murray Gell-Mann, Pierre Ramond, Richard Slansky
In the 1979 book *Supergravity* edited by P. van Nieuwenhuizen and D.Z. Freedman, Murray Gell-Mann, Pierre Ramond, and Richard Slangsky discuss complex spinors and unified theories. They note that self-coupled extended supergravity, especially for N = 8, is close to a unified theory, with no spin > 2 particles, and a spectrum that seems to match the desired elementary particles. However, the theory lacks the necessary spin 1 and spin 1/2 particles to match the observed spectrum. The theory also faces challenges in explaining the weak interaction bosons and the structure of the Standard Model. They explore the possibility of using complex spinor representations, such as the 16-dimensional spinor of $ SO_{10} $, which breaks down into $ 1 + \bar{5} + 10 $ of $ SU_5 $. This representation allows for a unified description of fermions, with the 10 giving Dirac masses and the 126 giving Majorana masses. However, the theory faces issues with neutrino masses and the need for a large Majorana mass to explain the observed neutrino mass. The authors also consider the $ SU_5 $ scheme, which has some successes in predicting the weak angle and the relation $ m_b = m_\tau $. However, it is considered a temporary expedient due to the arbitrariness of the Higgs bosons and the lack of C or P symmetry. They explore extensions of $ SU_5 $, such as $ E_6 $, which could provide a more unified framework. The discussion includes the idea of dynamical symmetry breaking, where the symmetry is broken through condensations, leading to massive gauge bosons and Goldstone bosons. The authors also consider the possibility of using generalized non-linear $ \sigma $-models to simulate such symmetry-breaking schemes. In conclusion, the authors argue that assigning left-handed fermions to a complex spinor representation of a gauge group like $ SO_{4n+2} $ or $ E_6 $ has attractive features, though it faces challenges. They suggest that the elementary fields of a unified theory may have only an indirect relation to the particles we observe today. The work highlights the complexity of unifying gravity with other forces and the need for further theoretical development.In the 1979 book *Supergravity* edited by P. van Nieuwenhuizen and D.Z. Freedman, Murray Gell-Mann, Pierre Ramond, and Richard Slangsky discuss complex spinors and unified theories. They note that self-coupled extended supergravity, especially for N = 8, is close to a unified theory, with no spin > 2 particles, and a spectrum that seems to match the desired elementary particles. However, the theory lacks the necessary spin 1 and spin 1/2 particles to match the observed spectrum. The theory also faces challenges in explaining the weak interaction bosons and the structure of the Standard Model. They explore the possibility of using complex spinor representations, such as the 16-dimensional spinor of $ SO_{10} $, which breaks down into $ 1 + \bar{5} + 10 $ of $ SU_5 $. This representation allows for a unified description of fermions, with the 10 giving Dirac masses and the 126 giving Majorana masses. However, the theory faces issues with neutrino masses and the need for a large Majorana mass to explain the observed neutrino mass. The authors also consider the $ SU_5 $ scheme, which has some successes in predicting the weak angle and the relation $ m_b = m_\tau $. However, it is considered a temporary expedient due to the arbitrariness of the Higgs bosons and the lack of C or P symmetry. They explore extensions of $ SU_5 $, such as $ E_6 $, which could provide a more unified framework. The discussion includes the idea of dynamical symmetry breaking, where the symmetry is broken through condensations, leading to massive gauge bosons and Goldstone bosons. The authors also consider the possibility of using generalized non-linear $ \sigma $-models to simulate such symmetry-breaking schemes. In conclusion, the authors argue that assigning left-handed fermions to a complex spinor representation of a gauge group like $ SO_{4n+2} $ or $ E_6 $ has attractive features, though it faces challenges. They suggest that the elementary fields of a unified theory may have only an indirect relation to the particles we observe today. The work highlights the complexity of unifying gravity with other forces and the need for further theoretical development.
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