Unification Paradigm GUT D10 Unification of strong weak

Unification Paradigm GUT D=10 • Unification of strong, weak and electromagnetic interactions within Grand Unified Theories is the new step in unification of all forces of Nature • Creation of a unified theory of everything based on string paradigm seems to be possible

What is SUSY? • Supersymmetry is a boson-fermion symmetry that is aimed to unify all forces in Nature including 2 7 gravity within a singe framework 9 1 n i s er Fir p a p st c n i e 1 7 19 c i s hy et y s p e l ic t r pa n • Modern views on supersymmetry in particle physics e d i vparadigm, though low energy e are based on string No manifestations of SUSY can be found (? ) at modern colliders and in non-accelerator experiments

Motivation of SUSY in Particle Physics l l l Unification with Gravity Unification of gauge couplings Solution of the hierarchy problem Dark matter in the Universe Superstrings Unification of matter (fermions) with forces (bosons) naturally arises from an attempt to unify gravity with the other interactions Local supersymmetry = general relativity !

Motivation of SUSY in Particle Physics l Unification of gauge couplings Running of the strong coupling

Motivation of SUSY RG Equations Input Unification of the Coupling Constants in the SM and in the MSSM Output SUSY yields unification!

Motivation of SUSY • Solution of the Hierarchy Problem Destruction of the hierarchy by radiative corrections SUSY may also explain the origin of the hierarchy due to radiative mechanism Cancellation of quadratic terms

Motivation of SUSY • Dark Matter in the Universe The flat rotation curves of spiral galaxies provide the most direct evidence for the existence of large amount of the dark matter. Spiral galaxies consist of a central bulge and a very thin disc, and surrounded by an approximately spherical halo of dark matter SUSY provides a candidate for the Dark matter – a stable neutral particle

Cosmological Constraints New precise cosmological data • Supernova Ia explosion • CMBR thermal fluctuations (recent news from WMAP ) Dark Matter in the Universe: Hot DM (not favoured by galaxy formation) Cold DM (rotation curves of Galaxies) SUSY

Superalgebra Grassmannian parameters SUSY Generators The only possible graded Lie algebra that mixes integer and half-integer spins and changes statistics

Quantum States Quantum states: Vacuum = Energy helicity State Expression vacuum # of states 1 1 -particle 2 -particle … N-particle Total # of states: … …

SUSY Multiplets scalar spinor helicity -1/2 0 1/2 # of states 1 2 1 Chiral multiplet helicity -1 -1/2 1 # of states 1 1 Vector multiplet spinor vector Members of a supermultiplet are called superpartners N=4 N=8 SUSY YM helicity λ = -1 # of states SUGRA helicity -2 – 3/2 – 1/2 0 1/2 1 3/2 2 λ = -2 # of states 1 spin -1 – 1/2 0 1/2 1 1 8 4 6 4 1 28 56 70 56 28 8 For renormalizable theories (YM) For (super)gravity 1

Simplest (N=1) SUSY Multiplets Bosons and Fermions come in pairs Spin 0 Spin 1/2 Spin 1 Spin 3/2 Spin 2

SUSY Transformation N=1 SUSY Chiral supermultiplet: spin=0 parameter of SUSY transformation (spinor) spin=1/2 Auxiliary field (unphysical d. o. f. needed to close SYSY algebra ) SUSY multiplets superfield Superfiled in Superspace Expansion over grassmannian parameter component fields

Gauge superfields Gauge superfield Field strength tensor Gauge transformation Wess-Zumino gauge physical fields Covariant derivatives

How to write SUSY Lagrangians 1 st step Take your favorite Lagrangian written in terms of fields 2 nd step Replace 3 rd step Replace Grassmannian integration in superspace

Superfield Lagrangians Grassmannian integration in superspace Matter fields Gauge transformation Gauge invariant interaction Superpotential

Gauge Invariant SUSY Lagrangian