The VLA Frontier Field Survey: A Comparison of the Radio and UV/Optical Size of 0.3 ≲ z ≲ 3 Star-forming Galaxies

o investigate the growth history of galaxies, we measure the rest-frame radio, ultraviolet (UV), and optical sizes of 98 radio-selected, star-forming galaxies (SFGs) distributed over 0.3 ≲ z ≲ 3 with a median stellar mass of $\mathrm{log}({M}_{\star }/{M}_{\odot })\approx 10.4$. We compare the size of galaxy stellar disks, traced by rest-frame optical emission, relative to the overall extent of star formation activity that is traced by radio continuum emission. Galaxies in our sample are identified in three Hubble Frontier Fields: MACS J0416.1−2403, MACS J0717.5+3745, and MACS J1149.5+2223. Radio continuum sizes are derived from 3 and 6 GHz radio images (≲0farcs6 resolution, ≈0.9 μJy beam−1 noise level) from the Karl G. Jansky Very Large Array. Rest-frame UV and optical sizes are derived using observations from the Hubble Space Telescope and the Advanced Camera for Surveys and Wide Field Camera 3 instruments. We find no clear dependence between the 3 GHz radio size and stellar mass of SFGs, which contrasts with the positive correlation between the UV/optical size and stellar mass of galaxies. Focusing on SFGs with $\mathrm{log}({M}_{\star }/{M}_{\odot })\gt 10$, we find that the radio/UV/optical emission tends to be more compact in galaxies with high star formation rates (≳100 M⊙ yr−1), suggesting that a central, compact starburst (and/or an active galactic nucleus) resides in the most luminous galaxies of our sample. We also find that the physical radio/UV/optical size of radio-selected SFGs with log(M⋆/M⊙) > 10 increases by a factor of 1.5–2 from z ≈ 3 to z ≈ 0.3, yet the radio emission remains two to three times more compact than that from the UV/optical. These findings indicate that these massive, radio-selected SFGs at 0.3 ≲ z ≲ 3 tend to harbor centrally enhanced star formation activity relative to their outer disks

The modular geometry of Random Regge Triangulations

We show that the introduction of triangulations with variable connectivity and fluctuating egde-lengths (Random Regge Triangulations) allows for a relatively simple and direct analyisis of the modular properties of 2 dimensional simplicial quantum gravity. In particular, we discuss in detail an explicit bijection between the space of possible random Regge triangulations (of given genus g and with N vertices) and a suitable decorated version of the (compactified) moduli space of genus g Riemann surfaces with N punctures. Such an analysis allows us to associate a Weil-Petersson metric with the set of random Regge triangulations and prove that the corresponding volume provides the dynamical triangulation partition function for pure gravity.Comment: 36 pages corrected typos, enhanced introductio

Glassy Random Matrix Models

This paper discusses Random Matrix Models which exhibit the unusual phenomena of having multiple solutions at the same point in phase space. These matrix models have gaps in their spectrum or density of eigenvalues. The free energy and certain correlation functions of these models show differences for the different solutions. Here I present evidence for the presence of multiple solutions both analytically and numerically. As an example I discuss the double well matrix model with potential $V(M)= -{\mu \over 2}M^2+{g \over 4}M^4$ where $M$ is a random $N\times N$ matrix (the $M^4$ matrix model) as well as the Gaussian Penner model with $V(M)={\mu\over 2}M^2-t \ln M$. First I study what these multiple solutions are in the large $N$ limit using the recurrence coefficient of the orthogonal polynomials. Second I discuss these solutions at the non-perturbative level to bring out some differences between the multiple solutions. I also present the two-point density-density correlation functions which further characterizes these models in a new university class. A motivation for this work is that variants of these models have been conjectured to be models of certain structural glasses in the high temperature phase.Comment: 25 pages, Latex, 7 Figures, to appear in PR

Size-selective nanoparticle growth on few-layer graphene films

We observe that gold atoms deposited by physical vapor deposition onto few layer graphenes condense upon annealing to form nanoparticles with an average diameter that is determined by the graphene film thickness. The data are well described by a theoretical model in which the electrostatic interactions arising from charge transfer between the graphene and the gold particle limit the size of the growing nanoparticles. The model predicts a nanoparticle size distribution characterized by a mean diameter D that follows a scaling law D proportional to m^(1/3), where m is the number of carbon layers in the few layer graphene film.Comment: 15 pages, 4 figure

Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models

We consider the hungry Volterra hierarchy from the view point of the multi boson KP hierarchy. We construct the hungry Volterra equation as the B\"{a}cklund transformations (BT) which are not the ordinary ones. We call them ``fractional '' BT. We also study the relations between the (discrete time) hungry Volterra equation and two matrix models. From this point of view we study the reduction from (discrete time) 2d Toda lattice to the (discrete time) hungry Volterra equation.Comment: 13 pages, LaTe

A Remark on the Renormalization Group Equation for the Penner Model

It is possible to extract values for critical couplings and gamma_string in matrix models by deriving a renormalization group equation for the variation of the of the free energy as the size N of the matrices in the theory is varied. In this paper we derive a ``renormalization group equation'' for the Penner model by direct differentiation of the partition function and show that it reproduces the correct values of the critical coupling and gamma_string and is consistent with the logarithmic corrections present for g=0,1.Comment: LaTeX, 5 pages, LPTHE-Orsay-94-5

Exact beta function from the holographic loop equation of large-N QCD_4

We construct and study a previously defined quantum holographic effective action whose critical equation implies the holographic loop equation of large-N QCD_4 for planar self-avoiding loops in a certain regularization scheme. We extract from the effective action the exact beta function in the given scheme. For the Wilsonean coupling constant the beta function is exacly one loop and the first coefficient agrees with its value in perturbation theory. For the canonical coupling constant the exact beta function has a NSVZ form and the first two coefficients agree with their value in perturbation theory.Comment: 42 pages, latex. The exponent of the Vandermonde determinant in the quantum effective action has been changed, because it has been employed a holomorphic rather than a hermitean resolution of identity in the functional integral. Beta function unchanged. New explanations and references added, typos correcte

An infinite genus mapping class group and stable cohomology

We exhibit a finitely generated group \M whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface \su of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus $g$ with $n$ boundary components, for any $g\geq 0$ and $n>0$. We construct a representation of \M into the restricted symplectic group ${\rm Sp_{res}}({\cal H}_r)$ of the real Hilbert space generated by the homology classes of non-separating circles on \su, which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first universal Chern class in H^2(\M,\Z) is the pull-back of the Pressley-Segal class on the restricted linear group ${\rm GL_{res}}({\cal H})$ via the inclusion ${\rm Sp_{res}}({\cal H}_r)\subset {\rm GL_{res}}({\cal H})$.Comment: 14p., 8 figures, to appear in Commun.Math.Phy

Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription

We find the exact non-perturbative expression for a simple Wilson loop of arbitrary shape for U(N) and SU(N) Euclidean or Minkowskian two-dimensional Yang-Mills theory regulated by the Wu-Mandelstam-Leibbrandt gauge prescription. The result differs from the standard pure exponential area-law of YM_2, but still exhibits confinement as well as invariance under area-preserving diffeomorphisms and generalized axial gauge transformations. We show that the large N limit is NOT a good approximation to the model at finite N and conclude that Wu's N=infinity Bethe-Salpeter equation for QCD_2 should have no bound state solutions. The main significance of our results derives from the importance of the Wu-Mandelstam-Leibbrandt prescription in higher-dimensional perturbative gauge theory.Comment: 7 pages, LaTeX, REVTE

Measurement of gamma p --> K+ Lambda and gamma p --> K+ Sigma0 at photon energies up to 2.6 GeV

The reactions gamma p --> K+ Lambda and gamma p --> K+ Sigma0 were measured in the energy range from threshold up to a photon energy of 2.6 GeV. The data were taken with the SAPHIR detector at the electron stretcher facility, ELSA. Results on cross sections and hyperon polarizations are presented as a function of kaon production angle and photon energy. The total cross section for Lambda production rises steeply with energy close to threshold, whereas the Sigma0 cross section rises slowly to a maximum at about E_gamma = 1.45 GeV. Cross sections together with their angular decompositions into Legendre polynomials suggest contributions from resonance production for both reactions. In general, the induced polarization of Lambda has negative values in the kaon forward direction and positive values in the backward direction. The magnitude varies with energy. The polarization of Sigma0 follows a similar angular and energy dependence as that of Lambda, but with opposite sign.Comment: 21 pages, 25 figures, submitted to Eur. Phys. J.