Gaugino Determinant in Supersymmetric Yang-Mills Theory

We resolve an ambiguity in the sign of the gaugino determinant in supersymmetric models. The result, that the gaugino determinant can be taken positive for all background gauge configurations, is necessary for application of QCD inequalities and lattice Monte Carlo methods to supersymmetric Yang-Mills models.Comment: 5 pages, LaTeX. Revised version to appear in Modern Physics Letters

Determination of Nonlinear Genetic Architecture using Compressed Sensing

We introduce a statistical method that can reconstruct nonlinear genetic models (i.e., including epistasis, or gene-gene interactions) from phenotype-genotype (GWAS) data. The computational and data resource requirements are similar to those necessary for reconstruction of linear genetic models (or identification of gene-trait associations), assuming a condition of generalized sparsity, which limits the total number of gene-gene interactions. An example of a sparse nonlinear model is one in which a typical locus interacts with several or even many others, but only a small subset of all possible interactions exist. It seems plausible that most genetic architectures fall in this category. Our method uses a generalization of compressed sensing (L1-penalized regression) applied to nonlinear functions of the sensing matrix. We give theoretical arguments suggesting that the method is nearly optimal in performance, and demonstrate its effectiveness on broad classes of nonlinear genetic models using both real and simulated human genomes.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:1408.342

Does the BICEP2 Observation of Cosmological Tensor Modes Imply an Era of Nearly Planckian Energy Densities?

BICEP2 observations, interpreted most simply, suggest an era of inflation with energy densities of order ($10^{16}\, {\rm GeV})^4$, not far below the Planck density. However, models of TeV gravity with large extra dimensions might allow a very different interpretation involving much more modest energy scales. We discuss the viability of inflation in such models, and conclude that existing scenarios do not provide attractive alternatives to single field inflation in four dimensions. Because the detection of tensor modes strengthens our confidence that inflation occurred, it disfavors models of large extra dimensions, at least for the moment.Comment: 4 pages, v3: version to appear in JHE

Instability of Quantum de Sitter Spacetime

Quantized fields (e.g., the graviton itself) in de Sitter (dS) spacetime lead to particle production: specifically, we consider a thermal spectrum resulting from the dS (horizon) temperature. The energy required to excite these particles reduces slightly the rate of expansion and eventually modifies the semiclassical spacetime geometry. The resulting manifold no longer has constant curvature nor time reversal invariance, and back-reaction renders the classical dS background unstable to perturbations. In the case of AdS, there exists a global static vacuum state; in this state there is no particle production and the analogous instability does not arise.Comment: 3 pages, v2: version to appear in JHE