Correlation functions of twist fields from Ward identities in the massive Dirac theory

We derive non-linear differential equations for correlation functions of U(1) twist fields in the two-dimensional massive Dirac theory. Primary U(1) twist fields correspond to exponential fields in the sine-Gordon model at the free-fermion point, and it is well-known that their vacuum two-point functions are determined by integrable differential equations. We extend part of this result to more general quantum states (pure or mixed) and to certain descendents, showing that some two-point functions are determined by the sinh-Gordon differential equations whenever there is translation and parity invariance, and the density matrix is the exponential of a bilinear expression in fermions. We use methods involving Ward identities associated to the copy-rotation symmetry in a model with two independent, anti-commuting copies. Such methods were used in the context of the thermally perturbed Ising quantum field theory model. We show that they are applicable to the Dirac theory as well, and we suggest that they are likely to have a much wider applicability to free fermion models in general. Finally, we note that our form-factor study of descendents twist fields combined with a CFT analysis provides a new way of evaluating vacuum expectation values of primary U(1) twist fields: by deriving and solving a recursion relation.Comment: 31 page

Can Supersymmetry Naturally Explain the Positron Excess?

It has often been suggested that the cosmic positron excess observed by the HEAT experiment could be the consequence of supersymmetric dark matter annihilating in the galactic halo. Although it is well known that evenly distributed dark matter cannot account for the observed excess, if substantial amounts of local dark matter substructure are present, the positron flux would be enhanced, perhaps to the observed magnitude. In this paper, we attempt to identify the nature of the substructure required to match the HEAT data, including the location, size and density of any local dark matter clump(s). Additionally, we attempt to assess the probability of such substructure being present. We find that if the current density of neutralino dark matter is the result of thermal production, very unlikely ($\sim 10^{-4}$ or less) conditions must be present in local substructure to account for the observed excess.Comment: Version accepted by Physical Review

Evaluation of Correlation Functions in Integrable Quantum Field Theories

The aim of this thesis is to explore correlation functions in two dimensional quantum field theories in two distinct ways. In part I a new method for calculating the differential equations parametrising the correlation functions of twist fields associated with the U (1) symmetry of the Dirac model is presented. While developing this method a new family of descendent twist fields are identified and their form factors calculated. This provides a novel way of calculating the vacuum expectation values of the primary twist fields and is shown to be entirely consistent with known results. The method of calculating the correlation functions of twist fields provides a parametrisation of several other correlation functions for various quantum states. Since this method relies on the Ward identities found in a double copy model it is hoped to have wider applications in other free fermion models. Part II concerns the truncated conformal space approach which has been developed to approximate perturbed conformal field theories. In this part the theory underpinning the approach is discussed and a working algorithm is developed for both bulk and boundary perturbed minimal models. The energy levels, mass gaps and one point functions of various models are computed using the truncated conformal space approach and are shown to be in good agreement with previous calculations. A possible method for using this approach to approximate two point functions in perturbed conformal field theories is discussed

Tidal Destruction of The First Dark Microhalos

We point out that the usual self-similarity in cold dark matter models is broken by encounters with individual normal galactic stars on sub-pc scale. Tidal heating and stripping must have redefined the density and velocity structures of the population of the Earth-mass dark matter halos, which are likely to have been the first bound structures to form in the Universe. The disruption rate depends strongly on {\it galaxy types} and the orbital distribution of the microhalos; in the Milky Way, stochastic radial orbits are destroyed first by stars in the triaxial bulge, microhalos on non-planar retrograde orbits with large pericenters and/or apocenters survive the longest. The final microhalo distribution in the {\it solar neighborhood} is better described as a superposition of filamentry microstreams rather than as a set of discrete spherical clumps in an otherwise homogeneous medium. We discuss its important consequences to our detections of microhalos by direct recoil signal and indirect annihilation signal.Comment: 13 pages, 3 figures, Astrophysical Journal, accepte

Ending Child Labor: A Role for International Human Rights Law (with Meron Makonnen)

All over the world, children are weaving carpets, cutting and polishingprecious stones, assembling shoes, cutting and sewing garments, mining fordiamonds, gold, silver, and tin, cutting sugar cane, harvesting fruit, coffee, andother crops, manufacturing toys, sporting goods and appliances, and workingas domestic servants, street vendors, herders, migrant workers, and prostitutes.These children often work long hours with dangerous tools and machines andare exposed to hazardous chemicals, polluted air, and infectious diseases.They are denied the education that is their right and deprived of prospects foreven minimally prosperous and healthy lives.The economic exploitation of children has generated an expanding set ofinternational legal standards designed to protect children from the harmful anddangerous effects of child labor. These standards, although well established,have suffered from many of the same practical weaknesses that have limitedthe effectiveness of international human rights law generally. This dilemma -strong legal norms but weak enforcement mechanisms - has contributed to arecent rise in private action to prevent child labor. These private initiativesutilize the standards embedded in international law and may, in turn, contributeto an evolution that will ultimately transform principles into effective,enforceable, legal norms

Which Law Applies to the Afghan Conflict?

Soviet armed forces have been directly engaged in combat in Afghanistan for more than 8 years. The level of international protest, sanctions and media coverage diminished after the initial outcry over the large-scale Soviet intervention in December 1979. With the conclusion in many diplomatic and professional quarters that the Soviet presence in Afghanistan would be of long duration, the focus of international disapproval shifted from the question whether the Soviet presence in Afghanistan was lawful or not to whether Soviet conduct in Afghanistan was lawful or not: fromjus ad bellum to jus in bello

The dark matter problem in disc galaxies

In the generic CDM cosmogony, dark-matter haloes emerge too lumpy and centrally concentrated to host observed galactic discs. Moreover, discs are predicted to be smaller than those observed. We argue that the resolution of these problems may lie with a combination of the effects of protogalactic discs, which would have had a mass comparable to that of the inner dark halo and be plausibly non-axisymmetric, and of massive galactic winds, which at early times may have carried off as many baryons as a galaxy now contains. A host of observational phenomena, from quasar absorption lines and intracluster gas through the G-dwarf problem, point to the existence of such winds. Dynamical interactions will homogenize and smooth the inner halo, and the observed disc will be the relic of a massive outflow. The inner halo expanded after absorbing energy and angular momentum from the ejected material. Observed discs formed at the very end of the galaxy formation process, after the halo had been reduced to a minor contributor to the central mass budget and strong radial streaming of the gas had died dow

Exploring a new definition of the green valley and its implications

The distribution of galaxies on a colour-magnitude diagram reveals a bimodality, featuring a passively evolving red sequence and a star-forming blue cloud. The region between these two, the Green Valley (GV), represents a fundamental transition where quenching processes operate. We exploit an alternative definition of the GV using the 4,000 Angstrom break strength, an indicator that is more resilient than colour to dust attenuation. We compare and contrast our GV definition with the traditional one, based on dust-corrected colour, making use of data from the Sloan Digital Sky Survey. Our GV selection - that does not need a dust correction and thus does not carry the inherent systematics - reveals very similar trends regarding nebular activity (star formation, AGN, quiescence) to the standard dust-corrected $^{0.1}(g-r)$. By use of high SNR stacked spectra of the quiescent GV subsample, we derive the simple stellar population (SSP) age difference across the GV, a rough proxy of the quenching timescale ($\Delta$t). We obtain an increasing trend with velocity dispersion ($\sigma$), from $\Delta$t$\sim$1.5Gyr at $\sigma$=100km/s, up to 3.5Gyr at $\sigma$=200km/s, followed by a rapid decrease in the most massive GV galaxies ($\Delta$t$\sim$1Gyr at $\sigma$=250km/s), suggesting two different modes of quenching, or the presence of an additional channel (rejuvenation).Comment: 5 pages, 4 figures. Accepted for publication in MNRAS Letter