Conifold geometries, topological strings and multi-matrix models

We study open B-model representing D-branes on 2-cycles of local Calabi--Yau geometries. To this end we work out a reduction technique linking D-branes partition functions and multi-matrix models in the case of conifold geometries so that the matrix potential is related to the complex moduli of the conifold. We study the geometric engineering of the multi-matrix models and focus on two-matrix models with bilinear couplings. We show how to solve this models in an exact way, without resorting to the customary saddle point/large N approximation. The method consists of solving the quantum equations of motion and using the flow equations of the underlying integrable hierarchy to derive explicit expressions for correlators. Finally we show how to incorporate in this formalism the description of several group of D-branes wrapped around different cycles.Comment: 35 pages, 5.3 and 6 revise

Candidates of z ~ 5.5--7 Galaxies in the HST Ultra Deep Field

We report results from our $z\simeq 5.5$--7 galaxy search in the HST Ultra Deep Field (UDF). Using the 400-orbit of ACS data, we found 108 plausible $5.5\leq z\leq 6.5$ (or $z\simeq 6$ for short) candidates to $m_{AB}(z_{850})=30.0$ mag. The contamination to the sample, either due to image artifacts or known types of astronomical objects, is likely negligible. The inferred surface densities of $z\simeq 6$ galaxies are consistent with our earlier predictions from $m_{AB}(z_{850})=26.5$ to 28.5 mag. After correcting for detection incompleteness, the counts of $z\simeq 6$ candidates to $m_{AB}(z_{850})=29.2$ mag suggests that the faint-end slope of the galaxy luminosity function (LF) at this redshift is likely between $\alpha=-1.8$ and -1.9, which is sufficient to account for the entire Lyman photon budget necessary to complete the reionization of the universe at $z\simeq 6$. We also searched for $z\simeq 6.5$--7 candidates using the UDF NICMOS data, and have found four candidates to $J_{110}=27.2$ mag. However, the infrared colors of three candidates cannot be easily explained by galaxies in this redshift range. We tentatively derive an upper limit to the cumulative surface density of galaxies at $z\simeq 7$ of 0.36 per arcmin$^2$ to $J_{110}=26.6$ mag, which suggest a noticeable drop in the LF amplitude from $z\simeq 6$ to $z\simeq 7$.Comment: accepted for publication in ApJL (submitted March 17 2004, accepted July 20 2004

Transversely Polarized Drell-Yan Process and Soft Gluon Resummation in QCD

We calculate the transverse-momentum $Q_T$ spectrum of the dilepton in the transversely polarized Drell-Yan process on the basis of the factorization theorem in QCD. We take into account universal logarithmically enhanced corrections in edge region of phase space by resumming multiple soft-gluon emissions to all orders in the small $Q_T$ region.Comment: 84 pages, 5 figures, Revised version published in Prog.Theor.Phy

Revisiting W gamma production at RHIC

We discuss W gamma production in polarized p p collisions at RHIC energy. We point out that the RHIC collider has two advantages over other hadron colliders to measure the characteristic feature of W gamma production: (1) the RHIC energy is not so high and (2) the polarized beams are available. We calculate the tree level cross section for W gamma production using a generic spin basis for W and discuss both the angular dependence and spin correlation.Comment: 14 pages, 15 Postscript figure

Classifying bases for 6D F-theory models

We classify six-dimensional F-theory compactifications in terms of simple features of the divisor structure of the base surface of the elliptic fibration. This structure controls the minimal spectrum of the theory. We determine all irreducible configurations of divisors ("clusters") that are required to carry nonabelian gauge group factors based on the intersections of the divisors with one another and with the canonical class of the base. All 6D F-theory models are built from combinations of these irreducible configurations. Physically, this geometric structure characterizes the gauge algebra and matter that can remain in a 6D theory after maximal Higgsing. These results suggest that all 6D supergravity theories realized in F-theory have a maximally Higgsed phase in which the gauge algebra is built out of summands of the types su(3), so(8), f_4, e_6, e_8, e_7, (g_2 + su(2)), and su(2) + so(7) + su(2), with minimal matter content charged only under the last three types of summands, corresponding to the non-Higgsable cluster types identified through F-theory geometry. Although we have identified all such geometric clusters, we have not proven that there cannot be an obstruction to Higgsing to the minimal gauge and matter configuration for any possible F-theory model. We also identify bounds on the number of tensor fields allowed in a theory with any fixed gauge algebra; we use this to bound the size of the gauge group (or algebra) in a simple class of F-theory bases.Comment: 28 pages, 2 figures, 1 appendix. v2: added references, minor changes; v3: two signs correcte

Galaxies Inside Stromgren Spheres of Luminous Quasars at z>6: Detection of The First Galaxies

The intrinsic Lyman-alpha emission lines of normal galaxies before reionization are much absorbed by the damping wing of the Gunn-Peterson trough, rendering their direct detection nearly impossible, if their intrinsic line widths are less than ~100km/s. High redshift luminous quasars prior to the completion of cosmological reionization at z~6, on the other hand, are capable of producing large HII regions around them (Stromgren spheres) to allow their intrinsic Lyman-alpha emission lines to be transmitted without overwhelming absorption (Cen & Haiman 2000). We suggest that targeted observations at the Stromgren spheres of known luminous quasars at z >= 6 would be able to detect Lyman-alpha emission lines of galaxies inside the Stromgren spheres largely unattenuated. A tunable, very narrowband filter of \Delta\lambda\over \lambda ~ 0.1% or a narrowband filter of \Delta\lambda\over \lambda ~1% with follow-up spectroscopic identifications will be required. Such observations could directly observe the sources of cosmological reionization including possibly the Pop III galaxies at z=6-20 by JWST. Possible applications include determinations of the ionization state of the intergalactic medium, the sizes of the Stromgren spheres, the ages of the quasars, the luminosity function of high redshift galaxies and its evolution, the spatial distribution of galaxies and its evolution, the biased distribution of galaxies around quasars and the anisotropy of quasar emission. Observations using Keck-class telescopes may already be made to enable a differentiation between a fully neutral and a 10% neutral intergalactic medium at z>6.Comment: Submitted to ApJ Letters, 10 page

The Major Sources of the Cosmic Reionizing Background at z ~ 6

In this paper, we address which sources contributed most of the reionizing photons. Our argument assumes that the reionization ended around z ~ 6 and that it was a relatively quick process, i.e., that there was a non-negligible fraction of neutral hydrogen in the Universe at somewhat earlier epochs. Starting from our earlier estimate of the luminosity function (LF) of galaxies at z ~ 6, we quantitatively show that the major sources of reionization are most likely galaxies with L < L*. Our approach allows us to put stronger constraints to the LF of galaxies at z ~ 6. To have the Universe completely ionized at this redshift, the faint-end slope of the LF should be steeper than $\alpha=-1.6$, which is the value measured at lower redshifts (z ~ 3), unless either the normalization (Phi*) of the LF or the clumping factor of the ionized hydrogen has been significantly underestimated. If Phi* is actually lower than what we assumed by a factor of two, a steep slope close to $\alpha=-2.0$ is required. Our LF predicts a total of 50 -- 80 z ~ 6 galaxies in the HST Ultra Deep Field (UDF) to a depth of AB=28.4 mag, which can be used to constraint both Phi* and $\alpha$. We conclude that the least luminous galaxies existing at this redshift should reach as low as some critical luminosity in order to accumulate the entire reionizing photon budget. On the other hand, the existence of significant amounts of neutral hydrogen at slightly earlier epochs, e.g. z ~ 7, requires that the least luminous galaxies should not be fainter than another critical value (i.e., the LF should cut-off at this point).Comment: ApJL in press (Jan 1, 2004 issue

Luminosity functions of Lyman-alpha emitters at z=6.5, and z=5.7: evidence against reionization at z=6

Lyman-alpha emission from galaxies should be suppressed completely or partially at redshifts beyond reionization. Without knowing the instrinsic properties of galaxies at z = 6.5, this attenuation is hard to infer in any one source, but can be infered from a comparison of luminosity functions of lyman-alpha emitters at redshifts just before and after reionization. We combine published surveys of widely varying depths and areas to construct luminosity functions at z=6.5 and 5.7, where the characteristic luminosity L_star and density phi_star are well constrained while the faint-end slope of the luminosity function is essentially unconstrained. Excellent consistency is seen in all but one published result. We then calculate the likelihood of obtaining the z=6.5 observations given the z=5.7 luminosity function with (A) no evolution and (B) an attenuation of a factor of three. Hypothesis (A) gives an acceptable likelihood while (B) does not. This indicates that the z=6.5 lyman-alpha lines are not strongly suppressed by a neutral intergalactic medium and that reionization was largely complete at z = 6.5.Comment: Submitted to Astrophysical Journal Letter

Constraints on First-Light Ionizing Sources from Optical Depth of the Cosmic Microwave Background

We examine the constraints on high-redshift star formation, ultraviolet and X-ray pre-ionization, and the epoch of reionization at redshift z_r, inferred from the recent WMAP-5 measurement, tau_e = 0.084 +/- 0.016, of the electron scattering optical depth of the cosmic microwave background (CMB). Half of this scattering can be accounted for by the optical depth, tau_e = 0.04-0.05, of a fully ionized intergalactic medium (IGM) at z < z_GP = 6-7, consistent with Gunn-Peterson absorption in neutral hydrogen. The required additional optical depth, Delta-tau_e = 0.03 +/- 0.02 at z > z_GP, constrains the ionizing contributions of first light sources. WMAP-5 also measured a significant increase in small-scale power, which lowers the required efficiency of star formation and ionization from mini-halos. Early massive stars (UV radiation) and black holes (X-rays) can produce a partially ionized IGM, adding to the residual electrons left from incomplete recombination. Inaccuracies in computing the ionization history, x_e(z), and degeneracies in cosmological parameters (Omega_m, Omega_b, sigma_8, n_s) add systematic uncertainty to the measurement and modeling of $\tau_e$. From the additional optical depth from sources at z > z_GP, we limit the star-formation efficiency, the rate of ionizing photon production for Pop III and Pop II stars, and the photon escape fraction, using standard histories of baryon collapse, minihalo star formation, and black-hole X-ray preionization.Comment: Greatly revised version, based on WMAP-5 results and new models. Accepted for ApJ (2008