Narrow Results

An algorithm to systematically and efficiently generate free fermionic heterotic string models was recently introduced.¹ This algorithm has been adopted by the Free Fermionic Model Construction (FFMC) program at Baylor University. As its first application, the algorithm is being applied to systematically generate the complete set of free fermionic heterotic string models with untwisted left-moving (worldsheet supersymmetric) sectors, up to continually advancing Layer and Order. Statistical analysis of this study will be reported in the near future. However, in a series of separate notes we will be reporting some of the more interesting models that appear along the way. In this, our first such note, we reveal a different string embedding of E₈ than is standard. That is, rather than realize E₈ via an SO(16) embedding, 248 = 120 + 128, we realize it via an SU(9) embedding, . This is obtained in a Layer 1, Order 6 model for which modular invariance itself dictates a gravitino sector accompany the gauge sector.

We consider an alternative derivation of the GSO Projection in the free fermionic construction of the weakly coupled heterotic string in terms of root systems, as well as the interpretation of the GSO Projection in this picture. We then present an algorithm to systematically and efficiently generate input sets (i.e. basic vectors) in order to study landscape statistics with minimal computational cost. For example, the improvement at order 6 is ≈10^-13 over a traditional brute force approach, and improvement increases with order. We then consider an example of statistics on a relatively simple class of models.

We refine a previous zeroth-order analysis of the nuclear properties of a supersymmetric (SUSY) universe with standard model particle content plus degenerate SUSY partners. No assumptions are made concerning the Higgs structure except we assume that the degenerate fermion/sfermion masses are nonzero. This alternate universe has been dubbed Susyria and it has been proposed that such a world may exist with zero vacuum energy in the string landscape.

From several points of view, it is strongly suggested that the current universe is unstable and will ultimately decay to one that is exactly supersymmetric (SUSY). The possibility that atoms and molecules form in this future universe requires that the degenerate electron/selectron mass is non-zero and hence that electroweak symmetry breaking (EWSB) survives the phase transition to exact SUSY. However, the Minimal Supersymmetric Standard Model (MSSM) and several of its extensions have no EWSB in the SUSY limit. Among the extended Higgs models that have been discussed, one stands out in this regard. The Higgs sector that is revealed at the Large Hadron Collider (LHC) will therefore have implications for the future universe. We also address the question as to whether the transition to the exact SUSY phase with EWSB is exothermic.

Motivated by the possibility of a string landscape, we re-examine tunneling of a scalar field across single/multiple barriers. Recent investigations have suggested modifications to the usual picture of false vacuum decay that leads to efficient and rapid tunneling in the landscape when certain conditions are met. This can be due to stringy effects (e.g. tunneling via the DBI action), or effects arising from the presence of multiple vacua (e.g. resonance tunneling). In this paper we discuss both DBI tunneling and resonance tunneling. We provide a QFT treatment of resonance tunneling using the Schrödinger functional approach. We also show how DBI tunneling for supercritical barriers can naturally lead to conditions suitable for resonance tunneling. We argue, using basic ideas from percolation theory, that tunneling can be rapid in a landscape where a typical vacuum has multiple decay channels, and discuss various cosmological implications. This rapidity vacuum decay can happen even if there are no resonance/DBI tunneling enhancements, solely due to the presence of a large number of decay channels. Finally, we consider various ways of circumventing a recent no-go theorem for resonance tunneling in quantum field theory.

An earlier paper points out that a quantum treatment of the string landscape is necessary. It suggests that the wave function of the universe is mobile in the landscape until the universe reaches a meta-stable site with its cosmological constant Λ₀ smaller than the critical value Λ_c, where Λ_c is estimated to be exponentially small compared to the Planck scale. Since this site has an exponentially long lifetime, it may well be today's universe. We investigate specific scenarios based on this quantum diffusion property of the cosmic landscape and find a plausible scenario for the early universe. In the last fast tunneling to the Λ₀(<Λ_c) site in this scenario, all energies are stored in the nucleation bubble walls, which are released to radiation only after bubble collisions and thermalization. So the Λ₀ site is chosen even if Λ₀ plus radiation is larger than Λ_c, as long as the radiation does not destabilize the Λ₀ vacuum. A consequence is that inflation must happen before this last fast tunneling, so the inflationary scenario that emerges naturally is extended brane inflation, where the brane motion includes a combination of rolling, fast tunnelings, slow-roll, hopping and percolation in the landscape. We point out that, in the brane world, radiation during nucleosynthesis are mostly on the standard model branes (brane radiation, as opposed to radiation in the bulk). This distinction may lead to interesting dynamics. We consider this paper as a road map for future investigations.

In what has become a standard eternal inflation picture of the string landscape there are many problematic consequences and a difficulty defining probabilities for the occurrence of each type of universe. One feature in particular that might be philosophically disconcerting is the infinite cloning of each individual and each civilization in infinite numbers of separated regions of the multiverse. Even if this is not ruled out due to causal separation one should ask whether the infinite cloning is a universal prediction of string landscape models or whether there are scenarios in which it is avoided. If a viable alternative cosmology can be constructed one might search for predictions that might allow one to discriminate experimentally between the models. We present one such scenario although, in doing so, we are forced to give up several popular presuppositions including the absence of a preferred frame and the homogeneity of matter in the universe. The model also has several ancillary advantages. We also consider the future lifetime of the current universe before becoming a light trapping region.

I review three attempts to explain the small value of the cosmological constant, and their connection to supersymmetry breaking. They are The String Landscape, Supersymmetric Large Extra Dimensions (SLED), and the Holographic Space–time Formalism invented by Fischler and myself.

We discuss various space–time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass.¹ In this alternative cosmology, the matter density was postulated to be a spatial delta function at the time of the big bang thereafter diffusing outward with constant total mass. This proposal explores a departure from standard assumptions that the big bang occurred everywhere at once or was just one of an infinite number of previous and later transitions.

The open inflationary scenario is attracting a renewed interest in the context of string landscape. Since there are a large number of metastable de Sitter vacua in string landscape, tunneling transitions to lower metastable vacua through the bubble nucleation occur quite naturally, which leads to a natural realization of open inflation. Recently, it was argued anthropically that string landscape would lead to an estimate of the density parameter in the range 0.998 ~ 0.9996. Although the deviation of Ω₀ from unity, the effect of this small deviation on the CMB anisotropies might be significant. If their estimate of the value of Ω₀ is correct, although yet there is no consensus about the problem of the probability measure, we might be able to discriminate the string landscape scenario from others. The effect of this small deviation on the large angle CMB anisotropies may be significant for large angle mode in tensor-type perturbation. We found that the wall fluctuation mode gives significant contribution even in string landscape and the square amplitude is determined only by the Hubble inside the bubble for large range of the potential parameters.

The open inflationary scenario is attracting a renewed interest in the context of string landscape. Since there are a large number of metastable de Sitter vacua in string landscape, tunneling transitions to lower metastable vacua through the bubble nucleation occur quite naturally, which leads to a natural realization of open inflation. We argued that the effect of the small deviation of the density parameter on the large angle CMB anisotropies may be significant for tensor-type perturbation in open inflation scenario. We found that the square amplitude for tensor-perturbation is determined not by the Hubble of the false vacuum directly but by that of the true vacuum even for sufficiently steep slope. Also we found that the tracking behavior can appear when one can choose the exponential-type potential with tuned parameters.