10^19 GeV
PLANCK SCALE
10^16 GeV
GUT SCALE
~1 TeV
SUSY BREAKING SCALE
100 GeV
ELECTROWEAK SCALE
ENERGY / TEMPERATURE OF THE UNIVERSE
GAUGINO CONDENSATION
Breaks Supersymmetry
GRAVITATIONAL CROSS-TALK
Gravity-Mediated, M_Planck-Suppressed (Gravitinos)
SYMMETRY BREAKING
Vacuum Expectation Value (VEV) Mechanism
⟨S⟩ = 0
UNSTABLE
⟨S⟩ ≠ 0
v
−v
V(ϕ)
ϕ
Singlet ⟨S⟩ Acquires VEV at Each Scale:
E6 → SO(10) → SU(5) → SM
COMPACTIFICATION
10D String → 4D Spacetime + 6D Calabi-Yau
6D
curled
10⁻³³ cm
Planck
scale
χ(CY₃) = 6 → 3 generations
h¹·¹ = 27 matter dims
COSMIC INFLATION
~10¹⁶ GeV — Both Sectors Inflate Space Simultaneously
Inflaton Candidates in E8×E8:
• Kähler/CY Moduli (extra-dimension shape fields)
• Singlet S flat direction (same field that breaks GUTs)
• Right-handed sneutrino ν̃_R (SUSY partner)
E8 × E8
HETEROTIC STRING THEORY
10 Dimensions • 496 Symmetries
Compactifies on Calabi-Yau Manifold → 4D Spacetime
Anomaly-Free in 10D (unique with SO(32))
HIDDEN SECTOR
MIRROR UNIVERSE
E8 • 248 Dimensions
Communicates Only via Gravity
VISIBLE SECTOR
OUR UNIVERSE BLUEPRINT
248 DIMS = 170 (Matter/Gravity) + 78 (Forces)
170 LEFTOVERS
GRAVITY & MATTER DIMS
• 162 Matter Dimensions
• 8 encode curvature of 6 extra dimensions
✓ OBS.
3 GENERATIONS
SO(8) TRIALITY SYMMETRY
• 27 Dims × 3 Families = 81 Dims
• (+ 81 Anti-Matter) = 162 Matter Total
• Calabi-Yau χ/2 = 3 (geometric origin)
E6 GUT
78 FORCE DIMENSIONS
• Contains all Unified Gauge Bosons
• Acts on the 162 Matter Dimensions
• SUSY enables gauge coupling unification here
PRED.
UNOBSERVED MATTER
THE 12 EXOTIC SLOTS (27 − 15 SM = 12)
• 1 Right-Handed Neutrino (Seesaw → light ν)
• 6 Heavy Exotic Quarks (D, D^c)
• 4 Exotic Leptons (Yields the Higgs)
• 1 Singlet (S) Field = 12 Total
THE SINGLET (S)
THE MASTER SWITCH
• Breaks GUT Symmetries
• Generates effective μ-term (NMSSM)
• Axion solves Strong CP problem
DARK MATTER: Axions (Unobserved)
SO(10) → SU(5) → SM
THE FORCE SPLINTERING
E6(78) → SO10(45) → SU5(24) → SM(12)
(66 forces decouple as universe cools)
Breaking: 27→16-plet (SO10) → S singlet (SU5)
CP-violating decays → Baryogenesis (matter/antimatter asymmetry)
PRED.
66 EXOTIC FORCES
78 (E6) − 12 (SM) = 66 GAUGE BOSONS
• 33 from E6: Z'/W' & Leptoquarks
• 21 from SO(10): X', Y' & Z' Bosons
• 12 from SU(5): X, Y (Proton Decay)
R-PARITY (Z2) — DISCRETE REMNANT
STABILIZES THE UNIVERSE
• Forbids Proton Decay • Makes LSP Dark Matter Stable
• Dim-5,6 decay allowed: τ_p ~10³⁴⁻³⁶ yr (testable at Hyper-K)
PRED.
SUPERSYMMETRY
SOFT MASSES AT ~1 TeV
• Every SM particle gets a superpartner
• Stabilizes Higgs mass (hierarchy problem)
• Required for gauge coupling unification
DARK MATTER: Lightest SUSY Particle (LSP)
✓ PARTIAL
HIGGS MECHANISM
ELECTROWEAK BREAKING
• Scalar superpartners of Exotic Leptons
• Contains the observed 125 GeV Higgs
• Breaks SU(2) × U(1) → U(1)_EM
• Gives Mass to W/Z Bosons & Fermions
PRED.
SHADOW MATTER
THE MIRROR UNIVERSE
• ~5x Mass of Visible Matter
• Interacts ONLY via Gravity
PRIMARY DARK MATTER COMPONENT
✓ CONF.
STANDARD MODEL
OUR LOW-ENERGY UNIVERSE
12 FORCE DIMS:
Gluons(8), W
±
/Z(3), γ(1)
15 MATTER DIMS:
Per Gen (15 × 3 = 45)
QUARKS (12)
LEPTONS (3)
SU(2) DOUBLET
u_L
d_L
} 6
SU(2) SINGLETS
u_R
} 3
d_R
} 3
R
G
B
= SU(3) color
SU(2) DOUBLET
ν_L
e_L
} 2
SU(2) SINGLET
e_R
} 1
= color singlet (no strong force)
12 quarks + 3 leptons = 15 Weyl fermions
SPACETIME & MATTER
GEOMETRIC TRIALITY
12 MISSING PER GEN
TRIGGERS BREAKING
DECOUPLED / HEAVY
SOFT SUSY MASSES
BREAKS EW SYMMETRY
Visualized by Prof. Andy Haas, NYU Physics, 2026