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main page: GrassmannCosmoFun2009**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

main page: GrassmannCosmoFun2009

- NICOLAI 14.09.2009
- Grassmann algebra key to supersymmetry
- anticommuting c-numbers
- Grassmann algebra splits into even (bosoic) and odd (fermionic) parts

- QFT: ...
- = formal device: anticommuting c-numbers are hard to visualise and impossible to measure
- extremely useful for description of fermions

- Berezin work: ...
- ... 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
- on-shell field theory (p^2 = m^2)
- S-matrix theory
- square Yang Mills amplitudes using KLT (Kawai Lewellen Tye (1986?)) rules
- Z.Bern http://www.livingreviews.org/lrr-2002-5

- 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

- superstringers relied on:

- Grassmann algebra key to supersymmetry
- Anthony LASENBY
- http://en.wikipedia.org/wiki/Geometric_algebra
- a geometric algebra approach can lead to a spherical model, with Omega_total about 1.01 to 1.02!

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png | 39c422a650e24a23413aae9dba4fe443.png | manage | 0.9 K | 15 Sep 2009 - 17:58 | UnknownUser | |

png | 4729a816ec42f7310d66c25b9af078a1.png | manage | 0.7 K | 15 Sep 2009 - 17:58 | UnknownUser |

Topic revision: r1 - 15 Sep 2009, BoudRoukema

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