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These are just rough notes - feel free to correct them, add links, etc. from the Grassmann ian Conference in Fundamental Cosmology (Grasscosmofun'09). These are not official proceedings. The speakers might even disagree that they said anything even vaguely related to what are in these online notes! Don't say you weren't warned.

Mon 14 Sep 2009

  • NICOLAI 14.09.2009
    • Grassmann algebra key to supersymmetry
      • anticommuting c-numbers
      • Grassmann algebra splits into even (bosonic) and odd (fermionic) parts
    • QFT: \{\phi(x),\phi\dagger(y)\} = \hbar \delta(x-y) ...
      • = formal device: anticommuting c-numbers are hard to visualise and impossible to measure
      • extremely useful for description of fermions
    • Berezin work: \frac{\partial}{ \partial\theta_i} \theta_j = \delta^i_j, ...
    • ... graded Lie algebras
    • supersymmetry - bosons - forces, fermions - matter
    • susy QM - q(t), \phi(t), lagrangian L(q,\dot{q},\phi,\dot{\phi}}
      • requires superpotential W(q)
      • Poisson brackets \{.,.\} or Dirac brackets
        • \{.,.\} = (i\hbar)^{-1} [commutator (fermions) or anticommutator (otherwise)]
      • Hamiltonian
    • Ward identities for correlators
    • Witten index *susy QFT - susy needs to be merged with symmetries like Poincare and internal symmetries
      • superalgebra = graded Lie algebra
      • N-extended susy for i,j=1,...,N merges spactime and internal symmetries when N \ge 2
    • representations (supermultiplets)
      • N = 8 supergravity - most symmetric - was favoured in 1970's
      • finiteness or not?
    • Einstein gravity is perturbatively non-renormalisable \Gamma^{(2)}_{div}...
      • for 2-loop; 3-loop or greater infinities
      • implies many people go to superstrings instead
    • counterterms needed to renormalise?
    • Counterterm gymnastics - N=8 supergravity
      • 2-loop corrections require e.g. 10^5 feynman diagram calculations
      • 3-loop corrections require e.g. 10^{20} feynman diagram calculations
    • using very different techniques, the latter is doable
    • 4-loop finiteness
      • get about 50 Mondrian-like diagrams
      • Why do we get a finite theory here? Big mystery
    • sociologically:
      • superstringers relied on:
        • N=8 supergravity divergent for \ge 3 loops
        • N=8 supergravity not viable for phenomenology
      • but (gauged) N=8 supergravity has a stationary point with residual SU(3) \times U(1) symmetry
  • Anthony LASENBY

-- BoudRoukema - 15 Sep 2009
Topic revision: r2 - 29 Oct 2009, BoudRoukema
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