Systematics of Aligned Axions

We describe a novel technique that renders theories of $N$ axions tractable, and more generally can be used to efficiently analyze a large class of periodic potentials of arbitrary dimension. Such potentials are complex energy landscapes with a number of local minima that scales as $\sqrt{N!}$, and so for large $N$ appear to be analytically and numerically intractable. Our method is based on uncovering a set of approximate symmetries that exist in addition to the $N$ periods. These approximate symmetries, which are exponentially close to exact, allow us to locate the minima very efficiently and accurately and to analyze other characteristics of the potential. We apply our framework to evaluate the diameters of flat regions suitable for slow-roll inflation, which unifies, corrects and extends several forms of "axion alignment" previously observed in the literature. We find that in a broad class of random theories, the potential is smooth over diameters enhanced by $N^{3/2}$ compared to the typical scale of the potential. A Mathematica implementation of our framework is available online.Comment: 68 pages, 17 figure

I\u27m just looking for a Lonesome Girl : Who\u27s just looking for a Lonesome Boy

https://digitalcommons.library.umaine.edu/mmb-vp/5874/thumbnail.jp

Low-temperature entropy in JT gravity

For ensembles of Hamiltonians that fall under the Dyson classification of random matrices with $\beta \in \{1,2,4\}$, the low-temperature mean entropy can be shown to vanish as $\langle S(T)\rangle\sim \kappa T^{\beta+1}$. A similar relation holds for Altland-Zirnbauer ensembles. JT gravity has been shown to be dual to the double-scaling limit of a $\beta =2$ ensemble, with a classical eigenvalue density $\propto e^{S_0}\sqrt{E}$ when $0 < E \ll 1$. We use universal results about the distribution of the smallest eigenvalues in such ensembles to calculate $\kappa$ up to corrections that we argue are doubly exponentially small in $S_0$.Comment: 17 page

Gravity as an ensemble and the moment problem

If a bulk gravitational path integral can be identified with an average of partition functions over an ensemble of boundary quantum theories, then a corresponding moment problem can be solved. We review existence and uniqueness criteria for the Stieltjes moment problem, which include an infinite set of positivity conditions. The existence criteria are useful to rule out an ensemble interpretation of a theory of gravity, or to indicate incompleteness of the gravitational data. We illustrate this in a particular class of 2D gravities including variants of the CGHS model and JT supergravity. The uniqueness criterium is relevant for an unambiguous determination of quantities such as $\overline{\log Z(\beta)}$ or the quenched free energy. We prove in JT gravity that perturbation theory, both in the coupling which suppresses higher-genus surfaces and in the temperature, fails when the number of boundaries is taken to infinity. Since this asymptotic data is necessary for the uniqueness problem, the question cannot be settled without a nonperturbative completion of the theory.Comment: 11+12 page

Direct observation of electron emission from grain boundaries in CVD diamond by PeakForce-controlled tunnelling atomic force microscopy

AbstractA detailed investigation of electron emission from a set of chemical vapour deposited (CVD) diamond films is reported using high-resolution PeakForce-controlled tunnelling atomic force microscopy (PF-TUNA). Electron field emission originates preferentially from the grain boundaries in low-conductivity polycrystalline diamond samples, and not from the top of features or sharp edges. Samples with smaller grains and more grain boundaries, such as nanocrystalline diamond, produce a higher emission current over a more uniform area than diamond samples with larger grain size. Light doping with N, B or P increases the grain conductivity, with the result that the emitting grain-boundary sites become broader as the emission begins to creep up the grain sidewalls. For heavy B doping, where the grains are now more conducting than the grain boundaries, emission comes from both the grain boundaries and the grains almost equally. Lightly P-doped diamond samples show emission from step-edges on the (111) surfaces. Emission intensity was time dependent, with the measured current dropping to ∼10% of its initial value ∼30h after removal from the CVD chamber. This decrease is ascribed to the build-up of adsorbates on the surface along with an increase in the surface conductivity due to surface transfer doping

Axion minima in string theory

We study the landscape of axion theories in compactifications of type IIB string theory on orientifolds of Calabi-Yau threefolds. In a sample of approximately 400,000 geometries we find that in the regime of perturbative control there are only a handful of distinct axion minima per geometry, despite there being infinitely many instanton contributions to the potential with unbounded charges. The ensemble we consider has numbers of axion fields ranging from 1 to 491, but the median number of distinct minima is 1, the mean number is 1.9 and the largest is 54. These small numbers of minima occur because the leading axion charge matrix is quite sparse, while the subleading corrections are increasingly exponentially suppressed as the charges increase. On their own, such potentials are nowhere near rich enough to be of interest anthropically. This is in stark contrast to potentials for which the charge matrix is less sparse or the hierarchies between the instanton contributions are less steep, where one can find $\mathcal{O}(10^{500})$ minima for $\mathcal{O}(500)$ axions. To generate a sufficiently large landscape from string compactifications our results indicate that one would need to rely on varying flux or topology, or to develop tools that allow one to go beyond the regime we can control with current techniques.Comment: 14+6 pages, 1 figur