1. HOLOGRAPHIC SPACE TIME AND SUPERSYMMETRY MBG-60 Conference Cambridge, UK April 2006

2. Green’s Theorem: A(ge) Duality A = 10/A + 26 + o(g S ) A = 10/A + 26 + o(g S ) Published in the Popular press as “60 is the new 30” Published in the Popular press as “60 is the new 30” Applies only to String Theorists Applies only to String Theorists Becker 2 + JS: Calculate Corrections through order g S 26 Becker 2 + JS: Calculate Corrections through order g S 26

3. HAPPY BIRTHDAY MICHAEL!

4. String Theory is Holographic Gauge Invariant Observables on Infinite Null/Timelike Surfaces. Inadequate for Cosmology, Where Boundary Unknown/Finite. Need Local Formulation Cf. GR: Fundamental Variable: Local, Gauge Variant Metric: g 

5. Holoscreens of a Causal Diamond Nested Causal Diamonds Define Observer World Line: Hilbert Space For Diamond Nested Causal Diamonds Define Observer World Line: Hilbert Space For Diamond

6. Dynamics from Compatibility Overlapping Sequences of Diamonds Share Tensor Factor of Hilbert Space Overlapping Sequences of Diamonds Share Tensor Factor of Hilbert Space

7. Variables of Quantum Gravity Pixel on Holoscreen: Spinor, By Cartan- Penrose Equation  y       = 0 Pixel on Holoscreen: Spinor, By Cartan- Penrose Equation  y       = 0 Quantize Via [S a (n), S b (m) ] + =  ab  mn Quantize Via [S a (n), S b (m) ] + =  ab  mn DOF of Pixel: Spin States of Massless Superparticle Exiting/Entering Pixel. Incorporate Compact Factors By Enlarging Algebra to Include Wrapped Brane Charges, Kaluza Klein Momenta and Monopole # Pixel Labels, m,n, Basis of Finite Dimensional Non- Commutative, Function Algebra of the Holographic Screen. S a (n) 2 Spinor Bundle Over Screen

8. Eleven Dimensions Take the function algebra of the holoscreen to converge to R[0,1]­ L(  ) Take the function algebra of the holoscreen to converge to R[0,1]­ L(  ) R[0,1] Hyperfinite II 1 Von Neumann Algebra (Projectors of Continuous Dim.) R[0,1] Hyperfinite II 1 Von Neumann Algebra (Projectors of Continuous Dim.) L[  ] Measurable Fcns. On S 9 L[  ] Measurable Fcns. On S 9 Operator Algebra © N ­ i S a i f a i (  ) For Any Number of Supergravitons Operator Algebra © N ­ i S a i f a i (  ) For Any Number of Supergravitons Consistency Equation for S-matrix??? Consistency Equation for S-matrix???

9. General Element of Algebra: A i ­ f i (  ) Spinor Bundle: S ´ {A i ­ q a i (  )} Unitary group: U i ­ f i (  ), U i y U i = 1, Gauge Symmetry of Quantum Theory S[q]: Map from Gauge Invariant Linear Functionals on S to Operator Algebra, Determined by Values on e i ­ q a i (  i ), e i e k =  ik e k Tr e k = p k ¸ 0 (Unique up to U i )  e i ­ S a i f a i (  ): Any Finite Sum, Permutation Statistics Gauge Symmetry

10. Super Poincare Algebra Lorentz Transformations: Conformal Group of S 9 Semi-Direct Product Out[R [0,1] ] Lorentz Transformations: Conformal Group of S 9 Semi-Direct Product Out[R [0,1] ] Super Translations: Q  ´  (p k ) 1/2 q a  (  k ) S a (k) q a  Conformal Killing Spinors of S 9 Kinematics of 11D SUGRA Fock Space Emerge. Need Dynamical Equation for the Scattering Matrix

11. Dynamics from Compatibility Overlapping Sequences of Diamonds Share Tensor Factor of Hilbert Space Overlapping Sequences of Diamonds Share Tensor Factor of Hilbert Space

12. A Solution of The Consistency Conditions Random Sequence of Hamiltonians For Each Observer: Irrelevant Perts of Free Random Model  S a (m) h mn S a (n) Random Sequence of Hamiltonians For Each Observer: Irrelevant Perts of Free Random Model  S a (m) h mn S a (n) Simple Overlap Conditions Simple Overlap Conditions Leads to Scaling Laws of Flat FRW Universe With p =  : Black Hole Fluid Leads to Scaling Laws of Flat FRW Universe With p =  : Black Hole Fluid Leads to Heuristic Picture of Our Universe Leads to Heuristic Picture of Our Universe Implies Future Asymptotic de Sitter Implies Future Asymptotic de Sitter

13. Fractal Bubbles of Normal Universe Embedded in p =  Fluid

14. In Normal Era p =  Interstices are Black Holes

15. Theory of Stable dS Space Two Hamiltonians [H, P 0 ] » ( P 0 / R). H spectrum · 1/R, Density e - R 2 Two Hamiltonians [H, P 0 ] » ( P 0 / R). H spectrum · 1/R, Density e - R 2 P 0 Eigenvalue ¼ Entropy Deficit of Eigenspace. Verified For Black Holes P 0 Eigenvalue ¼ Entropy Deficit of Eigenspace. Verified For Black Holes [  i A, (  y ) B j ] =  i j  A B N(N + 1) Matrix : Spinor Bundle Over Fuzzy Sphere [  i A, (  y ) B j ] =  i j  A B N(N + 1) Matrix : Spinor Bundle Over Fuzzy Sphere Identified Promising Candidates For Black Hole and Particle States Identified Promising Candidates For Black Hole and Particle States

16. Black Holes and Particles as Matrices

18. HAPPY BIRTHDAY MICHAEL!