Effective Potential on Fuzzy Sphere

The effective potential of quantized scalar field on fuzzy sphere is evaluated to the two-loop level. We see that one-loop potential behaves like that in the commutative sphere and the Coleman-Weinberg mechanism of the radiatively symmetry breaking could be also shown in the fuzzy sphere system. In the two-loop level, we use the heavy-mass approximation and the high-temperature approximation to perform the evaluations. The results show that both of the planar and nonplanar Feynman diagrams have inclinations to restore the symmetry breaking in the tree level. However, the contributions from planar diagrams will dominate over those from nonplanar diagrams by a factor N^2. Thus, at heavy-mass limit or high-temperature system the quantum field on the fuzzy sphere will behave like those on the commutative sphere. We also see that there is a drastic reduction of the degrees of freedom in the nonplanar diagrams when the particle wavelength is smaller than the noncommutativity scale.Comment: Latex 18 pages, some typos correcte

Entropy of gravitating systems: scaling laws versus radial profiles

Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which it is no longer an extensive quantity (it does not scale with system's size). To accomplish this, the methods introduced by Oppenheim [1] to characterize non-extensivity are used, suitably generalized to the case of gravitating systems subject to an external pressure. In particular when, far from the system's Schwarzschild limit, both area scaling for conventional entropy and inverse radius law for the temperature set in (i.e. the same properties of the corresponding black hole thermodynamical quantities), the entropy profile is found to behave like 1/r, being r the area radius inside the system. In such circumstances thus entropy heavily resides in internal layers, in opposition to what happens when area scaling is gained while approaching the Schwarzschild mass, in which case conventional entropy lies at the surface of the system. The information content of these systems, even if it globally scales like the area, is then stored in the whole volume, instead of packed on the boundary.Comment: 16 pages, 11 figures. v2: addition of some references; the stability of equilibrium configurations is readdresse

Lepto-mesons, Leptoquarkonium and the QCD Potential

We consider bound states of heavy leptoquark-antiquark pairs (lepto-mesons) as well as leptoquark-antileptoquark pairs (leptoquarkonium). Unlike the situation for top quarks, leptoquarks (if they exist) may live long enough for these hadrons to form. We study the spectra and decay widths of these states in the context of a nonrelativistic potential model which matches the recently calculated two-loop QCD potential at short distances to a successful phenomenological quarkonium potential at intermediate distances. We also compute the expected number of events for these states at future colliders.Comment: 12 pages, 1 figure, 3 tables, plain TeX, requires harvmac. References updated and minor clarifications made. To appear in Physics Letters

Leptogenesis from Pseudo-Scalar Driven Inflation

We examine recent claims for a considerable amount of leptogenesis, in some inflationary scenarios, through the gravitational anomaly in the lepton number current. We find that when the short distances contributions are properly included the amount of lepton number generated is actually much smaller.Comment: JHEP style, 11 pages. Corrected typ

A finite cutoff on the string worldsheet?

D-brane backgrounds are specified in closed string theories by holes with appropriate mixed Dirichlet and Neumann boundary conditions on the string worldsheet. As presently stated, the prescription defining D-brane backgrounds is such that the Einstein equation is not equivalent to the condition for scale invariance on the string worldsheet. A modified D-brane prescription is found, that leads to the desired equivalence, while preserving all known D-brane lore. A possible interpretation is that the worldsheet cutoff is finite. Possible connections to recent work of Maldacena and Strominger, and Gopakumar and Vafa are suggested.Comment: 7 pages, RevTex; v2: typos corrected, superstring calculation included, discussion expanded - to be published in Phys.Rev.

Fractal Holography: a geometric re-interpretation of cosmological large scale structure

The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit representation of information content, and also the value itself is a geometric signature of area. It is proposed that the fractal distribution of galaxies may thus be interpreted as a signature of holography (``fractal holography''), providing more support for current theories of holographic cosmologies. Implications for entropy bounds are addressed. In particular, because of spatial scale invariance in the matter distribution, it is shown that violations of the spherical entropy bound can be removed. This holographic condition instead becomes a rigid constraint on the nature of the matter density and distribution in the Universe. Inclusion of a dark matter distribution is also discussed, based on theoretical considerations of possible universal CDM density profiles.Comment: 13 pp, LaTeX. Revised version; to appear in JCA

Magnetic Wormholes and Vertex Operators

We consider wormhole solutions in $2+1$ Euclidean dimensions. A duality transformation is introduced to derive a new action from magnetic wormhole action of Gupta, Hughes, Preskill and Wise. The classical solution is presented. The vertex operators corresponding to the wormhole are derived. Conformally coupled scalars and spinors are considered in the wormhole background and the vertex operators are computed. ( To be published in Phys. Rev. D15)Comment: 18 pages of RevTex, preprint IP/BBSR/94-2

On the Thermal History of Calculable Gauge Mediation

Many messenger models with realistic gaugino masses are based on meta-stable vacua. In this work we study the thermal history of some of these models. Analyzing R-symmetric models, we point out that while some of the known messenger models clearly prefer the supersymmetric vacuum, there is a vast class of models where the answer depends on the initial conditions. Along with the vacuum at the origin, the high temperature thermal potential also possesses a local minimum far away from the origin. This vacuum has no analog at zero temperature. The first order phase transition from this vacuum into the supersymmetric vacuum is parametrically suppressed, and the theory, starting from that vacuum, is likely to evolve to the desired gauge-mediation vacuum. We also comment on the thermal evolution of models without R-symmetry.Comment: 22 pages. V2: Comments on the SM effects added. Minor corrections. Reference added. Valuable discussion with S. Abel, J. Jaeckel and V. Khoze acknowledged. V3: Types of EOGM explicitly defined in the introduction. Discussions about the phase transitions expanded. Typo corrected. Journal versio

Cleaning sky survey databases using Hough Transform and Renewal String approaches

Large astronomical databases obtained from sky surveys such as the SuperCOSMOS Sky Survey (SSS) invariably suffer from spurious records coming from artefactual effects of the telescope, satellites and junk objects in orbit around earth and physical defects on the photographic plate or CCD. Though relatively small in number these spurious records present a significant problem in many situations where they can become a large proportion of the records potentially of interest to a given astronomer. Accurate and robust techniques are needed for locating and flagging such spurious objects, and we are undertaking a programme investigating the use of machine learning techniques in this context. In this paper we focus on the four most common causes of unwanted records in the SSS: satellite or aeroplane tracks, scratches, fibres and other linear phenomena introduced to the plate, circular halos around bright stars due to internal reflections within the telescope and diffraction spikes near to bright stars. Appropriate techniques are developed for the detection of each of these. The methods are applied to the SSS data to develop a dataset of spurious object detections, along with confidence measures, which can allow these unwanted data to be removed from consideration. These methods are general and can be adapted to other astronomical survey data.Comment: Accepted for MNRAS. 17 pages, latex2e, uses mn2e.bst, mn2e.cls, md706.bbl, shortbold.sty (all included). All figures included here as low resolution jpegs. A version of this paper including the figures can be downloaded from http://www.anc.ed.ac.uk/~amos/publications.html and more details on this project can be found at http://www.anc.ed.ac.uk/~amos/sattrackres.htm

Brane Boxes, Anomalies, Bending and Tadpoles

Certain classes of chiral four-dimensional gauge theories may be obtained as the worldvolume theories of D5-branes suspended between networks of NS5-branes, the so-called brane box models. In this paper, we derive the stringy consistency conditions placed on these models, and show that they are equivalent to anomaly cancellation of the gauge theories. We derive these conditions in the orbifold theories which are T-dual to the elliptic brane box models. Specifically, we show that the expression for tadpoles for unphysical twisted Ramond-Ramond 4-form fields in the orbifold theory are proportional to the gauge anomalies of the brane box theory. Thus string consistency is equivalent to worldvolume gauge anomaly cancellation. Furthermore, we find additional cylinder amplitudes which give the $\beta$-functions of the gauge theory. We show how these correspond to bending of the NS-branes in the brane box theory.Comment: 14 pages, 3 epsf figures. Minor changes, references adde