One-Loop QCD Spin Chain and its Spectrum

We study the renormalization of gauge invariant operators in large Nc QCD. We compute the complete matrix of anomalous dimensions to leading order in the 't Hooft coupling and study its eigenvalues. Thinking of the mixing matrix as the Hamiltonian of a generalized spin chain we find a large integrable sector consisting of purely gluonic operators constructed with self-dual field strengths and an arbitrary number of derivatives. This sector contains the true ground state of the spin chain and all the gapless excitations above it. The ground state is essentially the anti-ferromagnetic ground state of a XXX1 spin chain and the excitations carry either a chiral spin quantum number with relativistic dispersion relation or an anti-chiral one with non-relativistic dispersion relation.Comment: 54 pages, v2: minor changes, references adde

Extensible records in the System E Framework and a new approach to object-oriented type inference

University of Technology, Sydney. Faculty of Engineering and Information Technology.Extensible records were proposed by Wand as a foundation for studying object-oriented type inference. One of their key benefits is that they allow for an elegant encoding of object-oriented inheritance, where one class of objects may be defined as an extension of another class of objects. However, every system of type inference designed for extensible records to date has been developed in the Hindley/Milner-style, a consequence being that polymorphism in these systems is not first-class and analysis is not strictly compositional. We argue that both of these features are necessary to retain the modelling and engineering benefits of traditional object-oriented languages such as Java: 1. Object-oriented modelling depends on the treatment of objects as first-class citizens, and this demands a type inference system capable of handling first-class polymorphism. 2. Object-oriented engineering encourages the separate development of software modules, and this should be supported by the type inference system with compositional analysis. Both of these features are present in a type system for the λ-calculus called System E, which supports first-class polymorphism via intersection types, and compositional type inference via expansion variables. However, research into System E has so far focused on refining and simplifying the formulation of expansion variables and exploring type inference algorithms with various properties. Meanwhile, the system has not yet been extended beyond the terms of the pure λ-calculus and it lacks many features that would be needed in a practical object-oriented language. In this dissertation, we combine System E with Wand’s extensible records resulting in a new approach to type inference for extensible records that better preserves the modelling and engineering benefits of object orientation stated above. The resulting system, called System Evcr, is significant because previous type inference systems, both for extensible records in particular, and also for object orientation in general, have at best preserved only one or the other of these two benefits, but never both of them simultaneously. System Evcr also makes a significant contribution to the work on System E, since it demonstrates for the first time that the System E’s expansion variables can be adapted to analyse programs whose term language extends beyond the pure λ-calculus. To demonstrate the potential use of System Evcr in object-oriented type inference, an implementation of our type inference algorithm was created and is shown to succeed on problem examples that previous systems either fail to analyse, or else fail to analyse compositionally

An Empirical Analysis of Empirical Legal Scholarship Production, 1990-2009

Inspired by the retirement of Professor Tom Ulen of the University of Illinois, the author considers the growth and development of empirical legal scholarship over two decades—a period of time that corresponds, not coincidentally, with Professor Ulen’s career. Starting in the 1990s when empirical scholarship had not yet “caught on,” the author first documents the increase in quantity of empirical scholarship over two decades. Next, the author applies a law and economics perspective to the recent surge in empirical scholarship, explaining that the trend has been fueled by an increase in the number of empirically trained scholars and also by increased demand for this type of scholarship. The author concludes by reflecting on Professor Ulen’s contribution to legal scholarship and suggests the time has come to ask not whether empirical legal scholarship has arrived but why it took so long to do so

Litigated Learning and the Limits of Law

Brown’s legacy and what it says about the efficacy of litigation as a vehicle to achieve social change mean different things to different people. Although popular mythology emphasizes Brown’s critical role in securing equal educational opportunity, careful reflection reveals that the decision’s legacy is anything but clear. A narrow focus on school desegregation suggests Brown’s legacy is aptly characterized as one of unfulfilled promise. A broader focus that extends to include subsequent equal educational opportunity activity such as the school finance litigation movement, however, casts positive light on Brown’s legacy. More important than completing interpretations of Brown’s legacy is what the decision implies for current and future efforts to secure greater educational equity through litigation. In this Article, I argue that Brown’s legacy does not bode well for future litigation efforts seeking to enhance the equal educational opportunity doctrine, principally due to how the doctrine has evolved during the past fifty years. Even if one concludes that Brown succeeded in the school desegregation context, the equal educational opportunity doctrine has changed during the past fifty years in ways that make it less amenable to litigation. Unlike past efforts, emerging reform efforts focus more directly on student academic achievement rather than race or school funding. Academic achievement implicates teaching and learning activities—activities located deeper inside schools and classrooms and further from litigation’s reach. If past education reformers and litigants found it difficult to penetrate factors located outside schools (school demographic profiles and funding levels), litigation efforts seeking to influence student achievement will encounter even greater difficulty. Student academic achievement’s insulation from even successful litigation underscores its inherent complexity, the salience of non-legal components and, more generally, structural limitations of law and litigation as tools to achieve desired social change. If my central claims are correct, the more complicated litigation efforts of the future will require manifestly greater effort. And greater effort alone will not insure success

Courting Trouble: Litigation, High-Stakes Testing, and Education Policy

High-stakes testing policies did not emerge in an education policy vacuum. Part I of this Article includes a brief description of the major high-stakes tests and their policy rationales. Part II surveys recent litigation challenging one distinct genre of high-stakes testing-high school exit exams. Two cases illustrate courts\u27 current posture toward legal challenges of exit exams. Part III reviews evidence of courts\u27 increased sensitivity to the policy consequences attributable to court decisions that interfere with the implementation of exit exams. Part IV concludes and notes the important normative questions raised by judges\u27 concerns with policy consequences flowing from their decisions

Courting Trouble: Litigation, High-Stakes Testing, and Education Policy

High-stakes testing policies did not emerge in an education policy vacuum. Part I of this Article includes a brief description of the major high-stakes tests and their policy rationales. Part II surveys recent litigation challenging one distinct genre of high-stakes testing-high school exit exams. Two cases illustrate courts\u27 current posture toward legal challenges of exit exams. Part III reviews evidence of courts\u27 increased sensitivity to the policy consequences attributable to court decisions that interfere with the implementation of exit exams. Part IV concludes and notes the important normative questions raised by judges\u27 concerns with policy consequences flowing from their decisions

Bounds on Compactness for LMXB Neutron Stars from X-ray Burst Oscillations

We have modelled X-ray burst oscillations observed with the Rossi X-ray Timing Explorer (RXTE) from two low mass X-ray binaries (LMXB): 4U 1636-53 with a frequency of 580 Hz, and 4U 1728-34 at a frequency of 363 Hz. We have computed least squares fits to the oscillations observed during the rising phase of bursts using a model which includes emission from either a single circular hot spot or a pair of circular antipodal hot spots on the surface of a neutron star. We model the spreading of the thermonuclear hot spots by assuming that the hot spot angular size grows linearly with time. We calculate the flux as a function of rotational phase from the hot spots and take into account photon deflection in the relativistic gravitational field of the neutron star assuming the exterior spacetime is the Schwarzschild metric. We find acceptable fits with our model and we use these to place constraints on the compactness of the neutron stars in these sources. For 4U 1636-53, in which detection of a 290 Hz sub-harmonic supports the two spot model, we find that the compactness (i.e., mass/radius ratio) is constrained to be M/R < 0.163 at 90% confidence (G = c = 1). This requires a relatively stiff equation of state (EOS) for the stellar interior. For example, if the neutron star has a mass of 1.4 Msun then its radius must be > 12.8 km. Fits using a single hot spot model are not as highly constraining. We discuss the implications of our findings for recent efforts to calculate the EOS of dense nucleon matter and the structure of neutron stars.Comment: 27 pages, 6 figures, AASTeX. Revised and expanded version. Resubmitted to Astrophysical Journa

A Search for X-Ray Flashes with XMM-Newton

We searched for X-ray flashes (XRFs) -- which we defined as ~10s duration transient X-ray events observable in the 0.4-15 keV passband -- in fields observed using XMM-Newton with the EPIC/pn detector. While we find two non-Poissonian events, the astrophysical nature of the events is not confirmed in fully simultaneous observations with the EPIC/MOS detectors, and we conclude that the events are anomalous to the EPIC/pn detector. We find a 90% upper limit on the number of flashes per sky per year at two different incoming flash fluxes: 4.0x10^9 events / sky / year for a flux of 7.1x10^-13 erg / cm^2 / s and 6.8x10^7 events / sky / year for 1.4x10^-11 erg / cm^2 / s. These limits are consistent with an extrapolation from the BeppoSAX/WFC XRF rate at much higher fluxes (about a factor of 10^5), assuming an homogenous population, and with a previous, more stringent limit derived from ROSAT pointed observations.Comment: Version accepted by MNRAS (minor changes

A note on fermions mesons in holographic QCD

We study the fermionic sector of a probe D8-brane in the supergravity background made of D4-branes compactified on a circle with supersymmetry broken explicitly by the boundary conditions. At low energies the dual field theory is effectively four-dimensional and has proved surprisingly successful in recovering qualitative and quantitative properties of QCD. We investigate fluctuations of the fermionic fields on the probe D8-brane and interpret these as mesinos (fermionic superpartners of mesons). We demonstrate that the masses of these modes are comparable to meson masses and show that their interactions with ordinary mesons are not suppressed