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 Implies dS space has finite dimensional Hilbert space

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

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 )

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

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 ~ M 3/2 # Disjoint Horizon volumes ~ M 1/2 In large block limit y i A -> y p 1/2 d ( W, W 0 ) y p 1/2 q a (W 0 ) are SUSY generators, where q a (W 0 ) are the Conformal Killing Spinors on S 2

Matrix Theory Decomposition of dS Pixel Operators

Maximum number of particles o(M 1/2 ) with max momentum ~ M 1/2 /R: M 3/2 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

Susy Breaking [Q, P_0 ] ~ L 1/4 (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 W 0 to enforce m 3/2 ~ L 1/4 CDL (ABJ) Meta-stability: e -A/4 A, area of cosmological horizon, Planck units: transition to low entropy state rather than instability

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 = m ISS Tr X PP ~ + g STr Y PP ~ + h S H u H d + f S 3 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

Dynamical Issues: (VEVs for and S) Related to properties of Kahler potential in N F = N C 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