Rotational Behaviors and Magnetic Field Evolution of Radio Pulsars

The observed long-term spin-down evolution of isolated radio pulsars cannot be explained by the standard magnetic dipole radiation with a constant braking torque. However how and why the torque varies still remains controversial, which is an outstanding problem in our understanding of neutron stars. We have constructed a phenomenological model of the evolution of surface magnetic fields of pulsars, which contains a long-term decay modulated by short-term oscillations; a pulsar's spin is thus modified by its magnetic field evolution. The predictions of this model agree with the precisely measured spin evolutions of several individual pulsars; the derived parameters suggest that the Hall drift and Hall waves in the NS crusts are probably responsible for the long-term change and short-term quasi-periodical oscillations, respectively. Many statistical properties of the timing noise of pulsars can be well re-produced with this model, including correlations and the distributions of the observed braking indices of the pulsars, which span over a range of more than 100 millions. We have also presented a phenomenological model for the recovery processes of classical and slow glitches, which can successfully model the observed slow and classical glitch events without biases.Comment: 6 pages, 9 figures, submitted to conference proceedings of SMFNS2013 (Strong electromagnetic field and neutron stars 2013

Tensor Hierarchy and Generalized Cartan Calculus in SL(3)×\timesSL(2) Exceptional Field Theory

We construct exceptional field theory for the duality group SL(3)$\times$SL(2). The theory is defined on a space with 8 `external' coordinates and 6 `internal' coordinates in the $(3,2)$ fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invariance can be made manifest by introducing higher form gauge fields and a so-called tensor hierarchy, which we systematically develop to much higher degree than in previous studies. To this end we introduce a novel Cartan-like tensor calculus based on a covariant nil-potent differential, generalizing the exterior derivative of conventional differential geometry. The theory encodes the full $D=11$ or type IIB supergravity, respectively.Comment: 49 page

A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua

We use Monte Carlo methods to explore the set of toric threefold bases that support elliptic Calabi-Yau fourfolds for F-theory compactifications to four dimensions, and study the distribution of geometrically non-Higgsable gauge groups, matter, and quiver structure. We estimate the number of distinct threefold bases in the connected set studied to be $\sim { 10^{48}}$. The distribution of bases peaks around $h^{1, 1}\sim 82$. All bases encountered after "thermalization" have some geometric non-Higgsable structure. We find that the number of non-Higgsable gauge group factors grows roughly linearly in $h^{1,1}$ of the threefold base. Typical bases have $\sim 6$ isolated gauge factors as well as several larger connected clusters of gauge factors with jointly charged matter. Approximately 76% of the bases sampled contain connected two-factor gauge group products of the form SU(3)$\times$SU(2), which may act as the non-Abelian part of the standard model gauge group. SU(3)$\times$SU(2) is the third most common connected two-factor product group, following SU(2)$\times$SU(2) and $G_2\times$SU(2), which arise more frequently.Comment: 38 pages, 22 figure

Non-toric bases for elliptic Calabi-Yau threefolds and 6D F-theory vacua

We develop a combinatorial approach to the construction of general smooth compact base surfaces that support elliptic Calabi-Yau threefolds. This extends previous analyses that have relied on toric or semi-toric structure. The resulting algorithm is used to construct all classes of such base surfaces $S$ with $h^{1, 1} (S) < 8$ and all base surfaces over which there is an elliptically fibered Calabi-Yau threefold $X$ with Hodge number $h^{2, 1} (X) \geq 150$. These two sets can be used todescribe all 6D F-theory models that have fewer than seven tensor multiplets or more than 150 neutral scalar fields respectively in their maximally Higgsed phase. Technical challenges to constructing the complete list of base surfaces for all Hodge numbers are discussed.Comment: 51 pages, 10 figure