Hidden symmetry of the quantum Calogero-Moser system

Hidden symmetry of the quantum Calogero-Moser system with the inverse-square potential is explicitly demonstrated in algebraic sense. We find the underlying algebra explaining the super-integrability phenomenon for this system. Applications to related multi-variable Bessel functions are also discussed.Comment: 16 pages, latex, no figure

T-Branes and Geometry

T-branes are a non-abelian generalization of intersecting branes in which the matrix of normal deformations is nilpotent along some subspace. In this paper we study the geometric remnant of this open string data for six-dimensional F-theory vacua. We show that in the dual M-theory / IIA compactification on a smooth Calabi-Yau threefold X, the geometric remnant of T-brane data translates to periods of the three-form potential valued in the intermediate Jacobian of X. Starting from a smoothing of a singular Calabi-Yau, we show how to track this data in singular limits using the theory of limiting mixed Hodge structures, which in turn directly points to an emergent Hitchin-like system coupled to defects. We argue that the physical data of an F-theory compactification on a singular threefold involves specifying both a geometry as well as the remnant of three-form potential moduli and flux which is localized on the discriminant. We give examples of T-branes in compact F-theory models with heterotic duals, and comment on the extension of our results to four-dimensional vacua.Comment: v2: 80 pages, 2 figures, clarifications and references added, typos correcte

The Footprint of F-theory at the LHC

Recent work has shown that compactifications of F-theory provide a potentially attractive phenomenological scenario. The low energy characteristics of F-theory GUTs consist of a deformation away from a minimal gauge mediation scenario with a high messenger scale. The soft scalar masses of the theory are all shifted by a stringy effect which survives to low energies. This effect can range from 0 GeV up to ~ 500 GeV. In this paper we study potential collider signatures of F-theory GUTs, focussing in particular on ways to distinguish this class of models from other theories with an MSSM spectrum. To accomplish this, we have adapted the general footprint method developed recently for distinguishing broad classes of string vacua to the specific case of F-theory GUTs. We show that with only 5 fb^(-1) of simulated LHC data, it is possible to distinguish many mSUGRA models and low messenger scale gauge mediation models from F-theory GUTs. Moreover, we find that at 5 fb^(-1), the stringy deformation away from minimal gauge mediation produces observable consequences which can also be detected to a level of order ~ +/- 80 GeV. In this way, it is possible to distinguish between models with a large and small stringy deformation. At 50 fb^(-1), this improves to ~ +/- 10 GeV.Comment: 85 pages, 37 figure

Exploring the Connection Between Star Formation and AGN Activity in the Local Universe

We study a combined sample of 264 star-forming, 51 composite, and 73 active galaxies using optical spectra from SDSS and mid-infrared (mid-IR) spectra from the Spitzer Infrared Spectrograph. We examine optical and mid-IR spectroscopic diagnostics that probe the amount of star formation and relative energetic contributions from star formation and an active galactic nucleus (AGN). Overall we find good agreement between optical and mid-IR diagnostics. Misclassifications of galaxies based on the SDSS spectra are rare despite the presence of dust obscuration. The luminosity of the [NeII] 12.8 \mu m emission-line is well correlated with the star formation rate (SFR) measured from the SDSS spectra, and this holds for the star forming, composite, and AGN-dominated systems. AGN show a clear excess of [NeIII] 15.6 \mu m emission relative to star forming and composite systems. We find good qualitative agreement between various parameters that probe the relative contributions of the AGN and star formation, including: the mid-IR spectral slope, the ratio of the [NeV] 14.3 \mu m to [NeII] \mu m 12.8 fluxes, the equivalent widths of the 7.7, 11.3, and 17 $\mu m$ PAH features, and the optical "D" parameter which measures the distance a source lies from the locus of star forming galaxies in the optical BPT emission-line diagnostic diagram. We also consider the behavior of the three individual PAH features by examining how their flux ratios depend upon the degree of AGN-dominance. We find that the PAH 11.3 \mu m feature is significantly suppressed in the most AGN-dominated systems.Comment: in review for ApJ. Updated to address referee's comments. 51 pages, 15 Figures, 13 Table

Local Starbursts in a Cosmological Context

In this contribution I introduce some of the major issues that motivate the conference, with an emphasis on how starbursts fit into the ``big picture''. I begin by defining starbursts in several different ways, and discuss the merits and limitations of these definitions. I will argue that the most physically useful definition of a starburst is its ``intensity'' (star formation rate per unit area). This is the most natural parameter to compare local starbursts with physically similar galaxies at high redshift, and indeed I will argue that local starbursts are unique laboratories to study the processes at work in the early universe. I will describe how NASA's GALEX mission has uncovered a rare population of close analogs to Lyman Break Galaxies in the local universe. I will then compare local starbursts to the Lyman-Break and sub-mm galaxies high redshift populations, and speculate that the multidimensional ``manifold'' of starbursts near and far can be understood largely in terms of the Schmidt/Kennicutt law and galaxy mass-metallicity relation. I will briefly summarize he properties of starburst-driven galactic superwinds and their possible implications for the evolution of galaxies and the IGM. These complex multiphase flows are best studied in nearby starbursts, where we can study the the hot X-ray gas that contains the bulk of the energy and newly produced metals.Comment: Proceedings of the Conference "Starbursts: Fropm 30 Doradus to Lyman Break Galaxies

On the Physical Origin of OVI Absorption-Line Systems

We present a unified analysis of the O{\sc vi} absorption-lines seen in the disk and halo of the Milky Way, high velocity clouds, the Magellanic Clouds, starburst galaxies, and the intergalactic medium. We show that these disparate systems define a simple relationship between the O{\sc vi} column density and absorption-line width that is independent of the Oxygen abundance over the range O/H $\sim$ 10% to twice solar. We show that this relation is exactly that predicted theoretically as a radiatively cooling flow of hot gas passes through the coronal temperature regime - independent of its density or metallicity (for O/H $\gtrsim$ 0.1 solar). Since most of the intregalactic O{\sc vi} clouds obey this relation, we infer that they can not have metallicities less than a few percent solar. In order to be able to cool radiatively in less than a Hubble time, the intergalactic clouds must be smaller than $\sim$1 Mpc in size. We show that the cooling column densities for the O{\sc iv}, O{\sc v}, Ne{\sc v}, and Ne{\sc vi} ions are comparable to those seen in O{\sc vi}. This is also true for the Li-like ions Ne{\sc viii}, Mg{\sc x}, and Si{\sc xii} (if the gas is cooling from $T \gtrsim 10^6$ K). All these ions have strong resonance lines in the extreme-ultraviolet spectral range, and would be accessible to $FUSE$ at $z \gtrsim$ 0.2 to 0.8. We also show that the Li-like ions can be used to probe radiatively cooling gas at temperatures an order-of-magnitude higher than where their ionic fraction peaks. We calculate that the H-like (He-like) O, Ne, Mg, Si, and S ions have cooling columns of $\sim10^{17}$ cm$^{-2}$. The O{\sc vii}, O{\sc viii}, and Ne{\sc ix} X-ray absorption-lines towards PKS 2155-304 may arise in radiatively cooling gas in the Galactic disk or halo.Comment: 25 pages, 5 figure