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Holography, de Sitter space and SUSY breaking

Holography, de Sitter space and SUSY breaking. Lindefest, Stanford, Mar 7, 2008. The Holographic Principle. ‘t Hooft, Fischler-Susskind-Bousso Covariant Entropy Bound Entropy bounded by maximal area on boundary of causal diamond TB, WF Entropy is that of max unc. Density matrix: ln dim H

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Holography, de Sitter space and SUSY breaking

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  1. Holography, de Sitter space and SUSY breaking Lindefest, Stanford, Mar 7, 2008

  2. The Holographic Principle • ‘t Hooft, Fischler-Susskind-Bousso • Covariant Entropy Bound • Entropy bounded by maximal area on boundary of causal diamond • TB, WF Entropy is that of max unc. Density matrix: ln dim H • Implies dS space has finite dimensional Hilbert space

  3. The Variables of Quantum Gravity: Pixels of a Holoscreen (or SUSY and the Holographic Screens) • Cartan Penrose Eqn l+ g0 g ml gml = 0 defines null direction l+ g0 g ml and plane transverse to it. Physical components Sa Light Cone Spinor • Up to local Lorentz transformation (connection implicit in Hamiltonian for Sa ) • Classical Scale Redundancy Broken by CAR • [Sa (m), Sb (n) ]+ = dab dmn

  4. Quantum Theory of 4D de Sitter Space • Holographic cosmology implies future of normal region is dS with c.c. determined by number of quantum states in initial defect (TB, Fischler) • Will outline (incomplete) quantum theory of eternal dS space, which describes asymptotic state of our universe (cf. Poincare invariant string theory of particle physics c. 1984-2000)

  5. Variables (Ignore compact internal space:wrong, does not give gravitons) • Spinor bundle over fuzzy two sphere • [yiA , y*jB ]+ = d IjdA B • M X (M + 1) matrix • TB, Fiol, Morisse, large M limit gives Hilbert space of single particle chiral supermultiplet with zero mass.

  6. More general limit gives Fock space: “Block” diagonalize • Different integers refer to disjoint horizon volumes • Block sizes vary, but total DOF in one horizon volume ~ M3/2 • # Disjoint Horizon volumes ~ M1/2 • In large block limit yiA -> y p1/2 d ( W , W0) • y p1/2 qa (W0) are SUSY generators, where • qa (W0) are the Conformal Killing Spinors on S2

  7. Matrix Theory Decomposition of dS Pixel Operators

  8. Maximum number of particles o(M1/2) with max momentum ~ M1/2 /R: M3/2 entropy • This coincides with field theory counting for states with no large black holes • Momentum restricts # of allowed spherical harmonics in wave function on sphere at infinity (pixelation) • Momentum p(1, W): p determined by size of matrix as in Matrix Theory • Can have particles of larger momentum, but fewer of them

  9. Susy Breaking • [Q, P_0 ] ~ L1/4 (Planck units) • Prescription for EFT : find LEFT with SUSY and R symm (zero c.c. limit). Add R breaking terms which lead to meta-stable SUSY breaking vacuum and tune W0 to enforce m3/2 ~ L1/4 • CDL (ABJ) Meta-stability: e-A/4 A, area of cosmological horizon, Planck units: transition to low entropy state rather than instability

  10. Best phenomenological model: the Pentagon • SU(5) X SU(1,2,3) SUSY gauge theory with std model augmented by (5,5*) + (5*,5) + (1,1) • W = mISS Tr X PP~ + g STr Y PP~ + h S Hu H d + f S3 • Solves flavor and CP problems of SUSY (but not strong CP). • No B and L violation thru d=5, apart from neutrino seesaw term • 1 loop unification, but couplings strong near unification scale and 2 loop analysis indicates Landau pole unless thresholds high

  11. Dynamical Issues: (VEVs for <PP~ > and S) • Related to properties of Kahler potential in NF = NC SUSY QCD (one parameter in large N limit). Required properties don’t violate general theorems • NLSP either RH slepton close to exptl bounds or neutralino • Tan b ~ 1 • No SUSY Dark Matter • PNGB of spontaneously broken penta-baryon number produced in flavor changing charged current weak decays. • Might also be the dark matter, but only if it is also responsible for baryon asymmetry of the universe

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