Holographic Multiverse

We explore the idea that the dynamics of the inflationary multiverse is encoded in its future boundary, where it is described by a lower dimensional theory which is conformally invariant in the UV. We propose that a measure for the multiverse, which is needed in order to extract quantitative probabilistic predictions, can be derived in terms of the boundary theory by imposing a UV cutoff. In the inflationary bulk, this is closely related (though not identical) to the so-called scale factor cutoff measure.Comment: 23 pages, 4 figures. Replaced to match published versio

Fuzzy Spheres in AdS/CFT Correspondence and Holography from Noncommutativity

We show that the existent fuzzy S^2 and S^4 models are natural candidates for the quantum geometry on the corresponding spheres in AdS/CFT correspondence. These models fit nicely the data from the dipole mechanism for the stringy exclusion principle. In the AdS_2 X S^2 case, we show that a wrapped fractional membrane can be used to count for the large ground state degeneracy. We also propose a fuzzy AdS_2 model whose fundamental commutation relation may underlie the UV/IR connection.Comment: 17 pages, one comment and reference adde

On 't Hooft's S-matrix Ansatz for quantum black holes

The S-matrix Ansatz has been proposed by 't Hooft to overcome difficulties and apparent contradictions of standard quantum field theory close to the black hole horizon. In this paper we revisit and explore some of its aspects. We start by computing gravitational backreaction effects on the properties of the Hawking radiation and explain why a more powerful formalism is needed to encode them. We then use the map bulk-boundary fields to investigate the nature of exchange algebras satisfied by operators associated with ingoing and outgoing matter. We propose and comment on some analogies between the non covariant form of the S-matrix amplitude and liquid droplet physics to end up with similarities with string theory amplitudes via an electrostatic analogy. We finally recall the difficulties that one encounters when trying to incorporate non linear gravity effects in 't Hooft's S-matrix and observe how the inclusion of higher order derivatives might help in the black hole microstate counting.Comment: 22 Pages. Latex Fil

Ab Initio Estimates of the Size of the Observable Universe

When one combines multiverse predictions by Bousso, Hall, and Nomura for the observed age and size of the universe in terms of the proton and electron charge and masses with anthropic predictions of Carter, Carr, and Rees for these masses in terms of the charge, one gets that the age of the universe should be roughly the inverse 64th power, and the cosmological constant should be around the 128th power, of the proton charge. Combining these with a further renormalization group argument gives a single approximate equation for the proton charge, with no continuous adjustable or observed parameters, and with a solution that is within 8% of the observed value. Using this solution gives large logarithms for the age and size of the universe and for the cosmological constant that agree with the observed values within 17%.Comment: 10 pages, LaTe

Freak observers and the measure of the multiverse

I suggest that the factor $p_j$ in the pocket-based measure of the multiverse, $P_j=p_j f_j$, should be interpreted as accounting for equilibrium de Sitter vacuum fluctuations, while the selection factor $f_j$ accounts for the number of observers that were formed due to non-equilibrium processes resulting from such fluctuations. I show that this formulation does not suffer from the problem of freak observers (also known as Boltzmann brains).Comment: 6 pages, no figures; references adde

High Energy Theorems at Large-N

Sum rules for products of two, three and four QCD currents are derived using chiral symmetry at infinite momentum in the large-N limit. These exact relations among meson decay constants, axialvector couplings and masses determine the asymptotic behavior of an infinite number of QCD correlators. The familiar spectral function sum rules for products of two QCD currents are among the relations derived. With this precise knowledge of asymptotic behavior, an infinite number of large-N QCD correlators can be constructed using dispersion relations. A detailed derivation is given of the exact large-N pion vector form factor and forward pion-pion scattering amplitudes.Comment: 34 pages TeX and mtexsis.tex, 10 figures (uses epsf

Unitary Quantum Physics with Time-Space Noncommutativity

In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schrodinger equation is studied. We prove in particular the following: suppose the Hamiltonian of a quantum mechanical particle on spacetime has no explicit time dependence, and the spatial coordinates commute in its noncommutative form (the only noncommutativity being between time and a space coordinate). Then the commutative and noncommutative versions of the Hamiltonian have identical spectra.Comment: 18 pages, published versio

Conformal Tightness of Holographic Scaling in Black Hole Thermodynamics

The near-horizon conformal symmetry of nonextremal black holes is shown to be a mandatory ingredient for the holographic scaling of the scalar-field contribution to the black hole entropy. This conformal tightness is revealed by semiclassical first-principle scaling arguments through an analysis of the multiplicative factors in the entropy due to the radial and angular degrees of freedom associated with a scalar field. Specifically, the conformal SO(2,1) invariance of the radial degree of freedom conspires with the area proportionality of the angular momentum sums to yield a robust holographic outcome.Comment: 23 pages, 1 figure. v2 & v3: expanded explanations and proofs, references added, typos corrected; v3: published versio

Of Bounces, Branes and Bounds

Some recent studies have considered a Randall-Sundrum-like brane world evolving in the background of an anti-de Sitter Reissner-Nordstrom black hole. For this scenario, it has been shown that, when the bulk charge is non-vanishing, a singularity-free ``bounce'' universe will always be obtained. However, for the physically relevant case of a de Sitter brane world, we have recently argued that, from a holographic (c-theorem) perspective, such brane worlds may not be physically viable. In the current paper, we reconsider the validity of such models by appealing to the so-called ``causal entropy bound''. In this framework, a paradoxical outcome is obtained: these brane worlds are indeed holographically viable, provided that the bulk charge is not too small. We go on to argue that this new finding is likely the more reliable one.Comment: 15 pages, Revtex; references added and very minor change