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Supersymmetric Grandunification: An Update

R. N. Mohapatra

TL;DR

This work surveys supersymmetric grand unification with emphasis on SUSY GUTs in the MSSM context, detailing SU(5) and SO(10) constructions, intermediate-scale unification, and Yukawa unification, while addressing key issues such as doublet–triplet splitting, proton decay, and R-parity. It additionally surveys alternative GUT groups (e.g., E6, SU(5)×SU(5), flipped SU(5), SU(6)) and explores how hidden-sector SUSY breaking mechanisms shape phenomenology. A substantial portion is devoted to the impact of string theory and extra dimensions on unification, including weakly and strongly coupled strings, large extra dimensions, and the resulting modifications to gauge-coupling evolution. The overarching message is that while SUSY GUTs offer elegant explanations for coupling unification and neutrino masses, their realization depends sensitively on the Higgs sector, symmetry-breaking patterns, and potential extensions via strings and extra dimensions, all of which introduce rich phenomenology and experimental tests, such as proton decay channels and lepton flavor violation.

Abstract

Recent developments in supersymmetric unified theories are reviewed, with particular emphasis on supersymmetric grand unification and a brief discussion of recent ideas about extra dimensions.

Supersymmetric Grandunification: An Update

TL;DR

This work surveys supersymmetric grand unification with emphasis on SUSY GUTs in the MSSM context, detailing SU(5) and SO(10) constructions, intermediate-scale unification, and Yukawa unification, while addressing key issues such as doublet–triplet splitting, proton decay, and R-parity. It additionally surveys alternative GUT groups (e.g., E6, SU(5)×SU(5), flipped SU(5), SU(6)) and explores how hidden-sector SUSY breaking mechanisms shape phenomenology. A substantial portion is devoted to the impact of string theory and extra dimensions on unification, including weakly and strongly coupled strings, large extra dimensions, and the resulting modifications to gauge-coupling evolution. The overarching message is that while SUSY GUTs offer elegant explanations for coupling unification and neutrino masses, their realization depends sensitively on the Higgs sector, symmetry-breaking patterns, and potential extensions via strings and extra dimensions, all of which introduce rich phenomenology and experimental tests, such as proton decay channels and lepton flavor violation.

Abstract

Recent developments in supersymmetric unified theories are reviewed, with particular emphasis on supersymmetric grand unification and a brief discussion of recent ideas about extra dimensions.

Paper Structure

This paper contains 37 sections, 145 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Brief introduction to the supersymmetric field theories
  3. The minimal supersymmetric standard model (MSSM)
  4. Why go beyond the MSSM ?
  5. Mechanisms for supersymmetry breaking
  6. Supersymmetric Left-Right model
  7. Digression on Mass scales
  8. Unification of Couplings
  9. Unification of Gauge Couplings (UGC)
  10. Unification Barometer
  11. Gauge coupling unification with intermediate scales before grand unification
  12. Yukawa unification
  13. Updating the discussion of mass scales in the light of grand unification
  14. Supersymmetric SU(5)
  15. Particle assignment and symmetry breaking
  16. ...and 22 more sections

Figures (4)

  • Figure 1: This figure shows the running of the superpartner masses from their GUT scale value and in particular note how the mass-square of $H_u$ turns negative at the weak scale triggering the breakdown of electroweak symmetry.
  • Figure 2: This figure shows the lack of unification of gauge couplings with standard model spectrum. $\alpha^{-1}_i$ is plotted against the mass scale and the values at the weak scale are the measures values from LEP and SLC as well as other experiments.
  • Figure 3: This figure shows the unification of gauge couplings with supersymmetric model spectrum. $\alpha^{-1}_i$ is plotted against the mass scale and the values at the weak scale are the measures values from LEP and SLC as well as other experiments.
  • Figure 4: This figure shows the running of the the gauge couplings for the minimal supersymmetric left-right model in the presence of one extra dimension with all gauge fields in the bulk.