Topology and Strings: Topics in N=2N=2

A review on topological strings and the geometry of the space of two dimensional theories. (Lectures given by C. Gomez at the Enrico Fermi Summer School, Varenna, July 1994)Comment: 61 pages, late

A Note on the String Analog of N=2N=2 Super-Symmetric Yang-Mills

A connection between the conifold locus of the type II string on the $W\:P_{11226}^4$ Calabi-Yau manifold and the geometry of the quantum moduli of $N = 2$ $SU(2)$ super Yang-Mills is presented. This relation is obtained from the anomalous behaviour of the $SU(2)$ super Yang-Mills special coordinates under $S$-duality transformation in $Sl(2;Z) / \Gamma_2$.Comment: 7 pages, Late

The homotopy type of the topological cobordism category

We define a cobordism category of topological manifolds and prove that if $d \neq 4$ its classifying space is weakly equivalent to $\Omega^{\infty -1} MTTop(d)$, where $MTTop(d)$ is the Thom spectrum of the inverse of the canonical bundle over $BTop(d)$. We also give versions with tangential structures and boundary. The proof uses smoothing theory and excision in the tangential structure to reduce the statement to the computation of the homotopy type of smooth cobordism categories due to Galatius-Madsen-Tillman-Weiss.Comment: 61 pages, 9 figures. Minor correction

One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations

In this paper we reconsider the Cachazo-He-Yuan construction (CHY) of the so called scattering amplitudes at one-loop, in order to obtain quadratic propagators. In theories with colour ordering the key ingredient is the redefinition of the Parke-Taylor factors. After classifying all the possible one-loop CHY-integrands we conjecture a new one-loop amplitude for the massless Bi-adjoint $\Phi^3$ theory. The prescription directly reproduces the quadratic propagators from of the traditional Feynman approach.Comment: 43 pages, new appendix added, few typos corrected. Accepted for publication in JHE

Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators

In this work we have studied the Kleiss-Kuijf relations for the recently introduced Parke-Taylor factors at one-loop in the CHY approach, that reproduce quadratic Feynman propagators. By doing this, we were able to identify the non-planar one-loop Parke-Taylor factors. In order to check that, in fact, these new factors can describe non-planar amplitudes, we applied them to the bi-adjoint $\Phi^3$ theory. As a byproduct, we found a new type of graphs that we called the non-planar CHY-graphs. These graphs encode all the information for the subleading order at one-loop, and there is not an equivalent of these in the Feynman formalism.Comment: 35 pages, typos corrected, references adde

Electromagnetic quasinormal modes of five-dimensional topological black holes

We calculate exactly the QNF of the vector type and scalar type electromagnetic fields propagating on a family of five-dimensional topological black holes. To get a discrete spectrum of quasinormal frequencies for the scalar type electromagnetic field we find that it is necessary to change the boundary condition usually imposed at the asymptotic region. Furthermore for the vector type electromagnetic field we impose the usual boundary condition at the asymptotic region and we discuss the existence of unstable quasinormal modes in the five-dimensional topological black holes.Comment: 16 pages. Already published in Revista Mexicana de Fisic

Constraints to the magnetospheric properties of T Tauri stars - II. The Mg II ultraviolet feature

The atmospheric structure of T Tauri Stars (TTSs) and its connection with the large scale outflow is poorly known. Neither the effect of the magnetically mediated inter- action between the star and the disc in the stellar atmosphere is well understood. The Mg II multiplet is a fundamental tracer of TTSs atmospheres and outflows, and is the strongest feature in the near-ultraviolet spectrum of TTSs. The International Ultraviolet Explorer and Hubble Space Telescope data archives provide a unique set to study the main physical compounds contributing to the line profile and to derive the properties of the line formation region. The Mg II profiles of 44 TTSs with resolution 13,000 to 30,000 are available in these archives. In this work, we use this data set to measure the main observables: flux, broadening, asymmetry, terminal velocity of the outflow, and the velocity of the Discrete Absorption Components. For some few sources repeated observations are available and variability has been studied. There is a warm wind that at sub-AU scales absorbs the blue wing of the Mg II profiles. The main result found in this work is the correlation between the line broadening, Mg II flux, terminal velocity of the flow and accretion rate. Both outflow and magnetospheric plasma contribute to the Mg II flux. The flux-flux correlation between Mg II and C IV or He II is confirmed; however, no correlation is found between the Mg II flux and the ultraviolet continuum or the H2 emission.Comment: 21 pages, 20 figure

Constraints to the magnetospheric properties of T Tauri stars. I. The C II], Fe II] and Si II] ultraviolet features

The C II] feature at ~2325 Angstrom is very prominent in the spectra of T Tauri stars (TTSs). This feature is a quintuplet of semiforbidden transitions excited at electron temperatures around 10,000 K that, together with the nearby Si II] and Fe II] features, provides a reliable optically thin tracer for accurate measurement of the plasma properties in the magnetospheres of TTSs. The spectra of 20 (out of 27) TTSs observed with the Space Telescope Imaging Spectrograph (STIS) on board the Hubble Space Telescope (HST) have good enough signal to noise ratio (S/N) at the C II] wavelength. For these stars we have determined electron densities (ne) and temperatures (Te) in the line emission region as well as the profile broadening (sigma). For most of the stars in the sample (17) we obtain 10^{4.1} < Te < 10^{4.5} K and 10^{8} < ne < 10^{12} cm^{-3}. These stars have suprathermal line broadening (35 < sigma < 165 km s^{-1}), except TW Hya and CY Tau with thermal line broadening. Both C II] line luminosity and broadening are found to correlate with the accretion rate. Line emission seems to be produced in the magnetospheric accretion flow, close to the disk. There are three exceptions: DG Tau, RY Tau and FU Ori. The line centroids are blueshifted indicating that the line emission in these three stars is dominated by the outflow.Comment: 13 pages, 15 figures, published in MNRAS minor change