T-Branes and Geometry

T-branes are a non-abelian generalization of intersecting branes in which the matrix of normal deformations is nilpotent along some subspace. In this paper we study the geometric remnant of this open string data for six-dimensional F-theory vacua. We show that in the dual M-theory / IIA compactification on a smooth Calabi-Yau threefold X, the geometric remnant of T-brane data translates to periods of the three-form potential valued in the intermediate Jacobian of X. Starting from a smoothing of a singular Calabi-Yau, we show how to track this data in singular limits using the theory of limiting mixed Hodge structures, which in turn directly points to an emergent Hitchin-like system coupled to defects. We argue that the physical data of an F-theory compactification on a singular threefold involves specifying both a geometry as well as the remnant of three-form potential moduli and flux which is localized on the discriminant. We give examples of T-branes in compact F-theory models with heterotic duals, and comment on the extension of our results to four-dimensional vacua.Comment: v2: 80 pages, 2 figures, clarifications and references added, typos correcte

T-Branes at the Limits of Geometry

Singular limits of 6D F-theory compactifications are often captured by T-branes, namely a non-abelian configuration of intersecting 7-branes with a nilpotent matrix of normal deformations. The long distance approximation of such 7-branes is a Hitchin-like system in which simple and irregular poles emerge at marked points of the geometry. When multiple matter fields localize at the same point in the geometry, the associated Higgs field can exhibit irregular behavior, namely poles of order greater than one. This provides a geometric mechanism to engineer wild Higgs bundles. Physical constraints such as anomaly cancellation and consistent coupling to gravity also limit the order of such poles. Using this geometric formulation, we unify seemingly different wild Hitchin systems in a single framework in which orders of poles become adjustable parameters dictated by tuning gauge singlet moduli of the F-theory model.Comment: v2: 65 pages, 6 figures, clarifications adde

Abortion in Northern Ireland: has the Rubicon been crossed?

On 7 June 2018, the Supreme Court delivered their long anticipated ruling on whether the abortion laws in Northern Ireland are compatible with the European Convention on Human Rights. Although the case was dismissed on procedural grounds, a majority of the court held that, obiter, the current Northern Irish law was incompatible with the right to respect for private and family life, protected by Article 8 ECHR, “insofar as it prohibits abortion in cases of rape, incest and fatal foetal abnormality”. This Supreme Court decision, seen alongside the May 2018 Irish referendum liberalising abortion, and the 5 June 2018 Parliamentary debate seeking to liberalise abortion laws in Northern Ireland and the rest of the UK, places renewed focus upon the abortion laws of Northern Ireland and Great Britain, which suggests that the ‘halfway house’ of the Abortion Act 1967 Act finally be close to being reformed to hand the decision of abortion to women themselves

The Lifetime and Powers of FR IIs in Galaxy Clusters

We have identified and studied a sample of 151 FR IIs found in brightest cluster galaxies (BCGs) in the MaxBCG cluster catalog with data from FIRST and NVSS. We have compared the radio luminosities and projected lengths of these FR IIs to the projected length distribution of a range of mock catalogs generated by an FR II model and estimate the FR II lifetime to be 1.9 x 10^8 yr. The uncertainty in the lifetime calculation is a factor of two, due primarily to uncertainties in the ICM density and the FR II axial ratio. We furthermore measure the jet power distribution of FR IIs in BCGs and find that it is well described by a log-normal distribution with a median power of 1.1 x 10^37 W and a coefficient of variation of 2.2. These jet powers are nearly linearly related to the observed luminosities, and this relation is steeper than many other estimates, although it is dependent on the jet model. We investigate correlations between FR II and cluster properties and find that galaxy luminosity is correlated with jet power. This implies that jet power is also correlated with black hole mass, as the stellar luminosity of a BCG should be a good proxy for its spheroid mass and therefore the black hole mass. Jet power, however, is not correlated with cluster richness, nor is FR II lifetime strongly correlated with any cluster properties. We calculate the enthalpy of the lobes to examine the impact of the FR IIs on the ICM and find that heating due to adiabatic expansion is too small to offset radiative cooling by a factor of at least six. In contrast, the jet power is approximately an order of magnitude larger than required to counteract cooling. We conclude that if feedback from FR IIs offsets cooling of the ICM, then heating must be primarily due to another mechanism associated with FR II expansion.Comment: 22 pages, 20 figures. Accepted to ApJ. Added minor clarifications throughout the paper and restructured section 6.2 in response to the referee. A brief video explaining the paper can be found at http://youtu.be/DOq85qUSU-

Measuring Lensing Magnification of Quasars by Large Scale Structure using the Variability-Luminosity Relation

We introduce a technique to measure gravitational lensing magnification using the variability of type I quasars. Quasars' variability amplitudes and luminosities are tightly correlated, on average. Magnification due to gravitational lensing increases the quasars' apparent luminosity, while leaving the variability amplitude unchanged. Therefore, the mean magnification of an ensemble of quasars can be measured through the mean shift in the variability-luminosity relation. As a proof of principle, we use this technique to measure the magnification of quasars spectroscopically identified in the Sloan Digital Sky Survey, due to gravitational lensing by galaxy clusters in the SDSS MaxBCG catalog. The Palomar-QUEST Variability Survey, reduced using the DeepSky pipeline, provides variability data for the sources. We measure the average quasar magnification as a function of scaled distance (r/R200) from the nearest cluster; our measurements are consistent with expectations assuming NFW cluster profiles, particularly after accounting for the known uncertainty in the clusters' centers. Variability-based lensing measurements are a valuable complement to shape-based techniques because their systematic errors are very different, and also because the variability measurements are amenable to photometric errors of a few percent and to depths seen in current wide-field surveys. Given the data volume expected from current and upcoming surveys, this new technique has the potential to be competitive with weak lensing shear measurements of large scale structure.Comment: Accepted for publication in Ap