SI3350 Grand Unified Theories 7.5 credits

Storförenande teorier

  • Education cycle

    Third cycle
  • Main field of study

  • Grading scale

    P, F

At present this course is not scheduled to be offered.

Intended learning outcomes

After completed course, the PhD student should be able to:

  • having the knowledge about the structure of the embedding of the SM gauge group and the relevant degrees of freedom into a unified scheme.
  • matching of the Standard Model parameters onto the 'microscopic' parameters of the underlying framework.
  • having the knowledge about the origin of the 'generic' predictions of the unified scenarios - the Weinberg angle, the proton instability, the preference of a TeV-scale supersymmetry.
  • emphasizing the differences between the supersymmetric and non-supersymmetric model building and the corresponding experimental constraints.

Course main content

Interactions in the standard model of particle physics and beyond. Open theoretical problems within the standard model. Hints for physics beyond the standard model. Basic introduction to group theory. Embedding the standard model gauge groups into a (semi-)simple gauge group. Dynamical consequences of grand unified theories. SU(5) as a GUT. Left-right symmetry. SO(10) models.


I. Standard Model of particle interactions & hints on physics beyond SM
⁃ Standard model of particle physics
⁃ open problems in SM
• hypercharge quantization in the SM & the "miracle" of anomaly cancellation
• the flavour problem of the SM (the Weinberg angle, Yukawa couplings, CKM mixing)
• the gauge hierarchy problem
• neutrino masses & mixing

II. Hints on physics beyond the (renormalizable) SM
- hints on new physics from neutrinos
• Majorana neutrinos, seesaw mechanism(s), d=5 Weinberg operator
• anomalies of U(1) of baryon and lepton number in SM & emergence of B-L
⁃ new physics due to d=6 operators - baryon number non-conservation
• B violation necessary for baryogenesis
• d=6 induced proton decay rate and the scale of the underlying physics
• L non-conservation as a lower bound on the B-L breakdown scale
⁃ hints on new physics from SU(2)xSU(3) running
• the concept of a running coupling
• running gauge couplings in Yang-Mills theories with fermions and scalars at one loop
⁃ potential benefits from having a unified gauge structure (Weinberg angle, Yukawa unification...)

III. Intermezzo 1: Elementary intro into Lie groups & representations
⁃ Lie groups and Lie algebras
⁃ simple, semisimple Lie algebras, compactness
⁃ subgroups, subalgebras, Cartan subalgebra, weights & roots
⁃ classification of simple Lie algebras, Dynkin diagrams
⁃ elements of representation theory
• real x complex representations, reducible x irreducible representations
• fundamental x antifundamental representations, adjoint representation
• index, symmetry features
⁃ examples - basic SU(N) representations, Young tableaux, SO(n) representations, spinors
⁃ decompositions or irreps with respect to subgroups, Clebsch-Gordan coefficients

IV. Embedding the SU(3)xSU(2)xU(1) of the SM into a (semi-)simple gauge group G
⁃ SM Cartans & need to look for rank 4 or more
⁃ need for complex representations
⁃ single simple rank 4 option - emergence of SU(5)
⁃ normalization issues & 'canonical' vs. 'physical' normalization of U(1) charges in GUTs
⁃ quantization of the SM (hyper)charge
⁃ Higgs sector, singlets with respect to a subgroup, Higgs mechanism

V. Dynamical consequences
⁃ d=6 proton decay (general considerations)
⁃ gauge coupling unification, decoupling under M_G & GUT-scale threshold corrections
⁃ hints on the minimal model(s) structure

VI. Minimal SU(5) model
⁃ structure
⁃ non-trivial predictions
• GUT-scale Weinberg angle
• third family Yukawa convergence
⁃ gauge running in minimal SU(5)
• a hint for supersymmetry

VII. Intermezzo 2: Supersymmetry & Supersymmetric GUTs
⁃ Supersymmetry basics
⁃ Minimal Supersymmetric Standard Model
⁃ SUSY flavour and CP issues, proton decay & R-parity, lepton flavour violation in SUSY
⁃ SUSY gauge running
⁃ tension between proton decay & SUSY CP and flavour vs. unification & hierarchy requirements

VIII. Minimal SUSY SU(5) model
⁃ structure
⁃ proton decay in minimal SUSY SU(5) model
⁃ troubles of minimal SUSY SU(5) (proton decay, neutrino sector, D-T finetunning)

IX. LR symmetry & Pati-Salam
⁃ U(1)B-L [ x SU(2)R ] as a gauge symmetry
⁃ the neutrino mass scale origin
⁃ Pati-Salam symmetry and lepton number as a fourth colour
⁃ alleviating proton decay in SUSY LR models

X. SO(10) models
⁃ spinors of SO(10)
⁃ SO(10) in SU(5) and Pati-Salam language
⁃ SUSYx non-SUSY setting
⁃ renormalizable x non-renormalizable seesaw
⁃ proton decay in SUSY SO(10)
• d=4 proton decay
• d=5 proton decay
• comparison to SUSY SU(5)

XI. Minimal renormalizable SUSY SO(10)
⁃ particle contents
⁃ R-parity as a gauge symmetry
⁃ type-II seesaw and naturally large lepton mixing
⁃ absolute neutrino mass scale issue

XII. Open problems & directions
⁃ doublet-triplet splitting
⁃ SUSY proton decay
⁃ perturbativity & proximity of the Planck scale
⁃ intermediate scales, gravitino problem in SUSY GUTs
⁃ SUSY SO(10) or non-SUSY SO(10)
⁃ split SUSY

XIII. Exotics (time permitting)
⁃ classical non-perturbative solutions & spontaneously broken gauge theories
• Nielsen-Olessen vortex in 2+1 dimensions, topological charges
• t'Hooft-Polyakov monopole in 3+1 dimensions
⁃ monopoles in GUTs
⁃ baryon decay catalysis
⁃ monopoles & inflation


Quantum field theory. Standard model of particle physics.


  • P.Langacker, Phys.Repts. 72 (1981)
  • R.Slansky, Phys.Repts. 79 (1981)
  • D.Bailin, A.Love, SUSY gauge field theories and string theory, ISBN 0750-302674
  • G.G.Ross, Grand Unified Theories, 1984, ISBN 0805-369678
  • R.N.Mohapatra, Unification & Supersymmetry, 1986/92, ISBN 0378-955348


  • INL1 - Assignment, 7.5, grading scale: P, F

Requirements for final grade

A set of homework exercises.

Offered by



Mattias Blennow (


Mattias Blennow <>


Course syllabus valid from: Spring 2019.
Examination information valid from: Spring 2019.