11.2 Supersymmetry and supergravity

Supersymmetry proposes a symmetry between bosons and fermions, extending the Standard Model with superpartners for each particle. This theory could solve the hierarchy problem, provide a dark matter candidate, and unify fundamental forces at high energies.

Supergravity combines supersymmetry with general relativity, introducing the gravitino as the superpartner of the graviton. It connects to string theory and offers a framework for addressing Standard Model shortcomings, including electroweak symmetry breaking and grand unification.

Supersymmetry Fundamentals

Symmetry between Bosons and Fermions

Top images from around the web for Symmetry between Bosons and Fermions

• 

  A fresh look for the standard model - Theory And Practice View original

  Is this image relevant?

• 

  Supersymmetry Archives - Universe Today View original

  Is this image relevant?

• 

  Fermion - Wikipedia, le encyclopedia libere View original

  Is this image relevant?

• 

  A fresh look for the standard model - Theory And Practice View original

  Is this image relevant?

• 

  Supersymmetry Archives - Universe Today View original

  Is this image relevant?

1 of 3

Top images from around the web for Symmetry between Bosons and Fermions

• 

  A fresh look for the standard model - Theory And Practice View original

  Is this image relevant?

• 

  Supersymmetry Archives - Universe Today View original

  Is this image relevant?

• 

  Fermion - Wikipedia, le encyclopedia libere View original

  Is this image relevant?

• 

  A fresh look for the standard model - Theory And Practice View original

  Is this image relevant?

• 

  Supersymmetry Archives - Universe Today View original

  Is this image relevant?

1 of 3

• Supersymmetry proposes a symmetry between bosons (particles with integer spin) and fermions (particles with half-integer spin)
  • Each particle in the Standard Model has a hypothetical superpartner with a spin differing by 1/2
    • For example, the electron (a fermion) would have a bosonic superpartner called the selectron
  • Supersymmetry transforms bosons into fermions and vice versa, extending the Poincaré algebra with anticommuting spinorial generators called supercharges

Broken Symmetry and the Hierarchy Problem

• Supersymmetry must be a broken symmetry since superpartners have not been observed at the same masses as their Standard Model counterparts
  • If supersymmetry were an exact symmetry, the superpartners would have the same mass as their Standard Model counterparts
• Supersymmetry can potentially solve the hierarchy problem in the Standard Model
  • The hierarchy problem arises from the vast difference between the weak scale (~100 GeV) and the Planck scale (~10^19 GeV)
  • Supersymmetry cancels quadratic divergences in the Higgs mass, stabilizing the weak scale against large quantum corrections

Dark Matter and Gauge Coupling Unification

• The lightest supersymmetric particle (LSP) is a candidate for dark matter if it is stable and electrically neutral
  • Stability can be ensured by imposing a discrete symmetry called R-parity, which distinguishes between ordinary particles and their superpartners
• Supersymmetry can lead to the unification of gauge couplings (strong, weak, and electromagnetic) at a high energy scale (~10^16 GeV)
  • This unification hints at the possibility of a grand unified theory (GUT) that describes all fundamental interactions, except gravity, within a single framework

Supersymmetric Field Theories

Construction and Properties

• Supersymmetric field theories are constructed by extending the Poincaré algebra with anticommuting spinorial generators called supercharges
  • The number of supercharges determines the amount of supersymmetry (N=1, N=2, etc.)
• The simplest supersymmetric field theory is the Wess-Zumino model, which consists of a complex scalar field and a Weyl fermion
  • The Wess-Zumino model is a toy model that demonstrates the basic features of supersymmetry
• Supersymmetric theories have improved ultraviolet behavior compared to their non-supersymmetric counterparts
  • Supersymmetry leads to cancellations between bosonic and fermionic loop diagrams, resulting in more convergent loop integrals and a better-behaved perturbative expansion

Supersymmetric Extensions of the Standard Model

• Supersymmetric gauge theories, such as the Minimal Supersymmetric Standard Model (MSSM), incorporate supersymmetry into the Standard Model
  • In the MSSM, each Standard Model particle has a superpartner with a spin differing by 1/2 (squarks, sleptons, gauginos, and higgsinos)
• The superpotential is a holomorphic function of the chiral superfields that determines the interactions and masses of the particles in a supersymmetric theory
  • The superpotential is constrained by the symmetries of the theory, such as gauge invariance and R-parity
• R-parity is a discrete symmetry in supersymmetric models that distinguishes between ordinary particles (R-parity even) and their superpartners (R-parity odd)
  • R-parity conservation has important consequences for proton stability (preventing rapid proton decay) and dark matter (ensuring the stability of the LSP)

Supersymmetry and Supergravity

Combining Supersymmetry and General Relativity

• Supergravity is a field theory that combines the principles of supersymmetry and general relativity
  • In supergravity, the graviton (the hypothetical quantum of the gravitational field) has a fermionic superpartner called the gravitino
• The number of supersymmetry generators determines the type of supergravity theory
  • N=1 supergravity is the simplest extension of general relativity with a single gravitino
  • N=8 supergravity is the maximal supergravity theory in four dimensions, with eight gravitinos

Connection to String Theory

• Supergravity theories can be constructed as the low-energy effective theories of string theory
  • String theory is a candidate for a quantum theory of gravity that describes fundamental particles as vibrating strings
• The local supersymmetry transformations in supergravity theories lead to the emergence of the gravitino and the associated gauge field, the spin connection
  • The gravitino is the gauge field associated with local supersymmetry transformations, similar to how the photon is the gauge field associated with local U(1) gauge transformations in electromagnetism

Supersymmetry Beyond the Standard Model

Addressing Shortcomings of the Standard Model

• Supersymmetry provides a framework for extending the Standard Model and addressing some of its shortcomings
  • The hierarchy problem: Supersymmetry stabilizes the weak scale against large quantum corrections by canceling quadratic divergences in the Higgs mass
  • The nature of dark matter: The lightest supersymmetric particle (LSP) can serve as a stable, weakly interacting massive particle (WIMP) dark matter candidate
• The Minimal Supersymmetric Standard Model (MSSM) is a well-studied extension of the Standard Model that incorporates supersymmetry with minimal additional particle content
  • The MSSM predicts a rich spectrum of new particles, such as squarks, sleptons, gauginos, and higgsinos, which can be searched for in high-energy collider experiments (LHC, future colliders)

Electroweak Symmetry Breaking and Grand Unification

• Supersymmetry can provide a mechanism for electroweak symmetry breaking through the Higgs sector
  • In the MSSM, the Higgs sector is extended to include two Higgs doublets, leading to five physical Higgs bosons (h, H, A, H±)
  • The lightest Higgs boson (h) in the MSSM can be compatible with the observed 125 GeV particle discovered at the LHC
• Supersymmetric grand unified theories (SUSY GUTs) can potentially explain the unification of gauge couplings and the origin of matter-antimatter asymmetry in the universe
  • SUSY GUTs embed the Standard Model gauge groups (SU(3)xSU(2)xU(1)) into a larger symmetry group, such as SU(5) or SO(10), at a high energy scale (~10^16 GeV)
  • The unification of gauge couplings in SUSY GUTs is more precise than in non-supersymmetric GUTs due to the modified renormalization group running of the couplings

Supersymmetry in Theories Beyond the Standard Model

• Supersymmetry is a key ingredient in many theories of physics beyond the Standard Model
  • String theory: Supersymmetry is necessary for the consistency of string theory, which aims to provide a unified description of all fundamental interactions, including gravity
  • Extra-dimensional models: Supersymmetry can be combined with the idea of extra spatial dimensions to address the hierarchy problem and provide novel dark matter candidates (Kaluza-Klein states)
• Supersymmetry provides a rich framework for exploring new physics and extending our understanding of the fundamental laws of nature
  • The discovery of supersymmetry would revolutionize our understanding of particle physics and have far-reaching implications for cosmology and the early universe