Monopoles, vortices and kinks in the framework of non-commutative geometry

Non-commutative differential geometry allows a scalar field to be regarded as a gauge connection, albeit on a discrete space. We explain how the underlying gauge principle corresponds to the independence of physics on the choice of vacuum state, should it be non-unique. A consequence is that Yang-Mills-Higgs theory can be reformulated as a generalised Yang-Mills gauge theory on Euclidean space with a $Z_2$ internal structure. By extending the Hodge star operation to this non-commutative space, we are able to define the notion of self-duality of the gauge curvature form in arbitrary dimensions. It turns out that BPS monopoles, critically coupled vortices, and kinks are all self-dual solutions in their respective dimensions. We then prove, within this unified formalism, that static soliton solutions to the Yang-Mills-Higgs system exist only in one, two and three spatial dimensions.Comment: 28 pages, Late

Modeling Transaction Data of Trade Direction and Estimation of Probability of Informed Trading

This paper implements the Asymmetric Autoregressive Conditional Duration (AACD) model of Bauwens and Giot (2003) to analyze irregularly spaced transaction data of trade direction, namely buy versus sell orders. We examine the influence of lagged transaction duration, lagged volume and lagged trade direction on transaction duration and direction. Our results are applied to estimate the probability of informed trading (PIN) based on the Easley, Hvidkjaer and OHara (2002) framework. Unlike the Easley- Hvidkjaer-OHara model, which uses the daily aggregate number of buy and sell orders, the AACD model makes full use of transaction data and allows for interactions between buy and sell orders.Autoregressive Conditional Duration, Market microstructure, Probability of Informed Trading, Transaction Data, Weibull Distribution

Information Content of Trade and Quote Imbalances, and the Hypothesis of Reverse Liquidity: Evidence from a fully automated exchange”, working paper

Abstract In this paper, we study the information contents of imbalances in trades and quotes emanated from an exchange resembling the one envisioned by Black (1971). We find dollar volume is more informative than number in measuring daily trading and quoting activities. Our measure of quote imbalance permits an investigation on the information asymmetry between market and limit orders. In case illegal insider trading does not occur regularly, we present a hypothesis of reverse liquidity as an alternative interpretation for our empirical findings. It could be that market-order traders charge an implicit liquidity premium for fulfilling the contrarian trading demand of limit-order traders. We suspect proprietary traders are filling the vacuum created by the absence of designated market makers and they provide reverse liquidity through their active trading

A Tale of Two Narrow-Line Regions: Ionization, Kinematics, and Spectral Energy Distributions for a Local Pair of Merging Obscured Active Galaxies

We explore the gas ionization and kinematics, as well as the optical--IR spectral energy distributions for UGC 11185, a nearby pair of merging galaxies hosting obscured active galactic nuclei (AGNs), also known as SDSS J181611.72+423941.6 and J181609.37+423923.0 (J1816NE and J1816SW, $z \approx 0.04$). Due to the wide separation between these interacting galaxies ($\sim 23$ kpc), observations of these objects provide a rare glimpse of the concurrent growth of supermassive black holes at an early merger stage. We use BPT line diagnostics to show that the full extent of the narrow line emission in both galaxies is photoionized by an AGN and confirm the existence of a 10-kpc-scale ionization cone in J1816NE, while in J1816SW the AGN narrow-line region is much more compact (1--2 kpc) and relatively undisturbed. Our observations also reveal the presence of ionized gas that nearly spans the entire distance between the galaxies which is likely in a merger-induced tidal stream. In addition, we carry out a spectral analysis of the X-ray emission using data from {\em XMM-Newton}. These galaxies represent a useful pair to explore how the [\ion{O}{3}] luminosity of an AGN is dependent on the size of the region used to explore the extended emission. Given the growing evidence for AGN "flickering" over short timescales, we speculate that the appearances and impact of these AGNs may change multiple times over the course of the galaxy merger, which is especially important given that these objects are likely the progenitors of the types of systems commonly classified as "dual AGNs."Comment: 15 pages, 10 figures, accepted by the Astrophysical Journa