COMPLEX SPINORS AND UNIFIED THEORIES

COMPLEX SPINORS AND UNIFIED THEORIES

1979 | Murray Gell-Mann, Pierre Ramond, Richard Slansky
The paper discusses the challenges and potential of unified theories, particularly focusing on complex spinors and their role in unified theories. The authors explore the possibility of a unified theory that combines gravity with supersymmetry, specifically self-coupled extended supergravity for \(N = 8\). They highlight the theory's consistency and the cancellation of cosmological constant contributions, but also point out the discrepancy between the predicted and observed particle spectrum, particularly the lack of certain spin 1 and spin 1/2 particles. The authors then delve into the construction of broken Yang-Mills theories, using \(SU_5\) as an example, and discuss the assignments of left-handed spin 1/2 fermions to reducible representations of \(SU_5\). They explore the implications of these assignments on fermion masses and the nature of neutrinos, suggesting that the Majorana mass term for the unobserved neutrino must be very large to avoid cosmological implications. The paper also examines the use of complex spinor representations in theories like \(SO_{10}\) and \(E_6\), and the challenges of dynamical spontaneous symmetry breaking. They propose that the left-handed fermions could be placed in a complex spinor representation of a gauge group \(SO_{4n+2}\) or \(E_6\), and discuss the constraints on fermion masses and the possibility of reconciling this with extended supergravity. Finally, the authors conclude by emphasizing the need for a more careful comparison between the ideas underlying extended supergravity and unified Yang-Mills theories, and the importance of understanding the relationship between the fundamental fields and the observed particles in a unified theory.The paper discusses the challenges and potential of unified theories, particularly focusing on complex spinors and their role in unified theories. The authors explore the possibility of a unified theory that combines gravity with supersymmetry, specifically self-coupled extended supergravity for \(N = 8\). They highlight the theory's consistency and the cancellation of cosmological constant contributions, but also point out the discrepancy between the predicted and observed particle spectrum, particularly the lack of certain spin 1 and spin 1/2 particles. The authors then delve into the construction of broken Yang-Mills theories, using \(SU_5\) as an example, and discuss the assignments of left-handed spin 1/2 fermions to reducible representations of \(SU_5\). They explore the implications of these assignments on fermion masses and the nature of neutrinos, suggesting that the Majorana mass term for the unobserved neutrino must be very large to avoid cosmological implications. The paper also examines the use of complex spinor representations in theories like \(SO_{10}\) and \(E_6\), and the challenges of dynamical spontaneous symmetry breaking. They propose that the left-handed fermions could be placed in a complex spinor representation of a gauge group \(SO_{4n+2}\) or \(E_6\), and discuss the constraints on fermion masses and the possibility of reconciling this with extended supergravity. Finally, the authors conclude by emphasizing the need for a more careful comparison between the ideas underlying extended supergravity and unified Yang-Mills theories, and the importance of understanding the relationship between the fundamental fields and the observed particles in a unified theory.
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