Download Holography, de Sitter space and SUSY breaking

Holography, de
Sitter space and
SUSY breaking
Lindefest, Stanford, Mar 7, 2008
The Holographic Principle
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‘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
The Variables of Quantum Gravity: Pixels of a
Holoscreen
SUSY and
the Holographic
(or
Cartan
Penrose
Eqn l+ Screens)
g0 g m l gm l = 0 defines
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null direction l+ g0 g m l 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 d mn
Quantum Theory of 4D de Sitter
Space
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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)
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Variables (Ignore compact internal
space:wrong, does not give gravitons)
Spinor bundle over fuzzy two sphere
[yiA , y* jB ]+ = d Ij 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
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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 q a (W0 ) are SUSY generators, where
q a (W0 ) are the Conformal Killing Spinors on
S2
Matrix Theory Decomposition of dS
Pixel Operators
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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
Susy Breaking
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[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
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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
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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