Renormalization Group and Dynamics of Supersymmetric Gauge Theories

We discuss questions related to renormalization group and to nonperturbative aspects of non-Abelian gauge theories with N=2 and/or N=1 supersymmetry. Results on perturbative and nonperturbative $\beta$ functions of these theories are reviewed, and new mechanisms of confinement and dynamical symmetry breaking recently found in a class of $SU(n_c)$, $USp(2n_c)$ and $SO(n_c)$ theories are discussed.Comment: 13 pages, 3 figures, uses ws-p9-75x6-50.cls. Lecture given at the Second Conference on the ERG, Rome 200

The dihadron fragmentation function and its evolution

Dihadron fragmentation functions and their evolution are studied in the process of $e^+e^-$ annihilation. Under the collinear factorization approximation and facilitated by the cut-vertex technique, the two hadron inclusive cross section at leading order (LO) is shown to factorize into a short distance parton cross section and a long distance dihadron fragmentation function. We provide the definition of such a dihadron fragmentation function in terms of parton matrix elements and derive its DGLAP evolution equation at leading log. The evolution equation for the non-singlet quark fragmentation function is solved numerically with a simple ansatz for the initial condition and results are presented for cases of physical interest.Comment: 27 pages, 2 column, Revtex4, 21 figure

Sp(N) higher-derivative F-terms via singular superpotentials

We generalize the higher-derivative F-terms introduced by Beasley and Witten (hep-th/0409149) for SU(2) superQCD to Sp(N) gauge theories with fundamental matter. We generate these terms by integrating out massive modes at tree level from an effective superpotential on the chiral ring of the microscopic theory. Though this superpotential is singular, its singularities are mild enough to permit the unambiguous identification of its minima, and gives sensible answers upon integrating out massive modes near any given minimum.Comment: 15 pages, 6 figure

On singular effective superpotentials in supersymmetric gauge theories

We study N=1 supersymmetric SU(2) gauge theory in four dimensions with a large number of massless quarks. We argue that effective superpotentials as a function of local gauge-invariant chiral fields should exist for these theories. We show that although the superpotentials are singular, they nevertheless correctly describe the moduli space of vacua, are consistent under RG flow to fewer flavors upon turning on masses, and also reproduce by a tree-level calculation the higher-derivative F-terms calculated by Beasely and Witten (hep-th/0409149) using instanton methods. We note that this phenomenon can also occur in supersymmetric gauge theories in various dimensions.Comment: 21 pages, 5 figures; minor errors correcte

Topological-charge anomalies in supersymmetric theories with domain walls

Domain walls in 1+2 dimensions are studied to clarify some general features of topological-charge anomalies in supersymmetric theories, by extensive use of a superfield supercurrent. For domain walls quantum modifications of the supercharge algebra arise not only from the short-distance anomaly but also from another source of long-distance origin, induced spin in the domain-wall background, and the latter dominates in the sum. A close look into the supersymmetric trace identity, which naturally accommodates the central-charge anomaly and its superpartners, shows an interesting consequence of the improvement of the supercurrent: Via an improvement the anomaly in the central charge can be transferred from induced spin in the fermion sector to an induced potential in the boson sector. This fact reveals a dual character, both fermionic and bosonic, of the central-charge anomaly, which reflects the underlying supersymmetry. The one-loop superfield effective action is also constructed to verify the anomaly and BPS saturation of the domain-wall spectrum.Comment: 8 pages, Revte

Halcyornis toliapicus (aves: Lower Eocene, England) indicates advanced neuromorphology in Mesozoic Neornithes

Our recent X-ray micro computer-tomographic (μCT) investigations of Prophaethon shrubsolei and Odontopteryx toliapica from the Lower Eocene London Clay Formation of England revealed the avian brain to have been essentially modern in form by 55 Ma, but that an important vision-related synapomorphy of living birds, the eminentia sagittalis of the telencephalon, was poorly developed. This evidence suggested that the feature probably appeared close to the end of the Mesozoic. Here we use μCT analysis to describe the endocranium of Halcyornis toliapicus, also from the London Clay Formation. The affinities of Halcyornis have been hotly debated, with the taxon referred to the Charadriiformes (Laridae), Coraciiformes (Alcedinidae, and its own family Halcyornithidae) and most recently that Halcyornithidae may be a possible senior synonym of Pseudasturidae (Pan-Psittaciformes). Unlike Prophaethon and Odontopteryx, the eminentia sagittalis of Halcyornis is strongly developed and comparable to that of living species. Like those London Clay taxa, the eminentia sagittalis occupies a rostral position on the telencephalon. The senses of Halcyornis appear to have been well developed. The length of the cochlear duct of the inner ear indicates a hearing sensitivity within the upper range of living species, and enlarged olfactory lobes suggest a reasonable reliance on sense of smell. The optic nerves were especially well developed which, together with the strong development of the eminentia sagittalis, indicates a high degree of visual specialization in Halcyornis. The advanced development of the eminentia sagittalis further supports a Mesozoic age for the appearance of this structure and associated neural architectural complexity found in extant Aves. The eminentia sagittalis of living Psittaciformes is situated caudally on the telencephalon, making a Pan-Psittaciformes relationship unlikely for Halcyorni

How do we decide what to do? Resting-state connectivity patterns and components of self-generated thought linked to the development of more concrete personal goals

Human cognition is not limited to the available environmental input but can consider realities that are different to the here and now. We describe the cognitive states and neural processes linked to the refinement of descriptions of personal goals. When personal goals became concrete, participants reported greater thoughts about the self and the future during mind-wandering. This pattern was not observed for descriptions of TV programmes. Connectivity analysis of participants who underwent a resting-state functional magnetic resonance imaging scan revealed neural traits associated with this pattern. Strong hippocampal connectivity with ventromedial pre-frontal cortex was common to better-specified descriptions of goals and TV programmes, while connectivity between hippocampus and the pre-supplementary motor area was associated with individuals whose goals were initially abstract but became more concrete over the course of the experiment. We conclude that self-generated cognition that arises during the mind-wandering state can allow goals to be refined, and this depends on neural systems anchored in the hippocampus