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

Nilpotent Networks and 4D RG Flows

Starting from a general $\mathcal{N} = 2$ SCFT, we study the network of $\mathcal{N} = 1$ SCFTs obtained from relevant deformations by nilpotent mass parameters. We also study the case of flipper field deformations where the mass parameters are promoted to a chiral superfield, with nilpotent vev. Nilpotent elements of semi-simple algebras admit a partial ordering connected by a corresponding directed graph. We find strong evidence that the resulting fixed points are connected by a similar network of 4D RG flows. To illustrate these general concepts, we also present a full list of nilpotent deformations in the case of explicit $\mathcal{N} = 2$ SCFTs, including the case of a single D3-brane probing a $D$- or $E$-type F-theory 7-brane, and 6D $(G,G)$ conformal matter compactified on a $T^2$, as described by a single M5-brane probing a $D$- or $E$-type singularity. We also observe a number of numerical coincidences of independent interest, including a collection of theories with rational values for their conformal anomalies, as well as a surprisingly nearly constant value for the ratio $a_{\mathrm{IR}} / c_{\mathrm{IR}}$ for the entire network of flows associated with a given UV $\mathcal{N} = 2$ SCFT. The $\texttt{arXiv}$ submission also includes the full dataset of theories which can be accessed with a companion $\texttt{Mathematica}$ script.Comment: v2: 73 pages, 12 figures, clarifications and references adde

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

T-Branes at the Limits of Geometry

Singular limits of 6D F-theory compactifications are often captured by T-branes, namely a non-abelian configuration of intersecting 7-branes with a nilpotent matrix of normal deformations. The long distance approximation of such 7-branes is a Hitchin-like system in which simple and irregular poles emerge at marked points of the geometry. When multiple matter fields localize at the same point in the geometry, the associated Higgs field can exhibit irregular behavior, namely poles of order greater than one. This provides a geometric mechanism to engineer wild Higgs bundles. Physical constraints such as anomaly cancellation and consistent coupling to gravity also limit the order of such poles. Using this geometric formulation, we unify seemingly different wild Hitchin systems in a single framework in which orders of poles become adjustable parameters dictated by tuning gauge singlet moduli of the F-theory model.Comment: v2: 65 pages, 6 figures, clarifications adde

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

The Discovery of an Active Galactic Nucleus in the Late-type Galaxy NGC 3621: Spitzer Spectroscopic Observations

We report the discovery of an Active Galactic Nucleus (AGN) in the nearby SAd galaxy NGC 3621 using Spitzer high spectral resolution observations. These observations reveal the presence of [NeV] 14 um and 24 um emission which is centrally concentrated and peaks at the position of the near-infrared nucleus. Using the [NeV] line luminosity, we estimate that the nuclear bolometric luminosity of the AGN is ~ 5 X 10^41 ergs s^-1, which corresponds based on the Eddington limit to a lower mass limit of the black hole of ~ 4 X 10^3 Msun. Using an order of magnitude estimate for the bulge mass based on the Hubble type of the galaxy, we find that this lower mass limit does not put a strain on the well-known relationship between the black hole mass and the host galaxy's stellar velocity dispersion established in predominantly early-type galaxies. Mutli-wavelength follow-up observations of NGC 3621 are required to obtain more precise estimates of the bulge mass, black hole mass, accretion rate, and nuclear bolometric luminosity. The discovery reported here adds to the growing evidence that a black hole can form and grow in a galaxy with no or minimal bulge.Comment: 5 pages, 7 figures, Accepted for publication in ApJ Letter

The Spatial Clustering of Low Luminosity AGN

We present the first multi-parameter analysis of the narrow line AGN clustering properties. Estimates of the two-point correlation function (CF) based on SDSS DR2 data reveal that Seyferts are clearly less clustered than normal galaxies, while the clustering amplitude (r_0) of LINERs is consistent with that of the parent galaxy population. The similarities in the host properties (color and concentration index) of Seyferts and LINERs suggest that the difference in their r_0 is not driven by the morphology-density relation. We find that the luminosity of [O I] emission shows the strongest influence on AGN clustering, with low L([O I]) sources having the highest r_0. This trend is much stronger than the previously detected dependence on L([O III]), which we confirm. There is a strong correspondence between the clustering patterns of objects of given spectral type and their physical properties. LINERs, which exhibit high r_0, show the lowest luminosities and obscuration levels, and relatively low gas densities (n_e), suggesting that these objects harbor black holes that are relatively massive yet weakly active or inefficient in their accretion, probably due to the insufficiency of their fuel supply. Seyferts, which have low r_0, are luminous and show large n_e, suggesting that their black holes are less massive but accrete quickly and efficiently enough to clearly dominate the ionization. The low r_0 of the H II galaxies can be understood as a consequence of both the morphology-density and star formation rate-density relations, however, their spectral properties suggest that their centers hide amidst large amounts of obscuring material black holes of generally low mass whose activity remains relatively feeble. Our own Milky Way may be a typical such case.[abridged]Comment: 27 pages, color figures, some are severely degraded in resolution, emulateapj. See http://www.physics.drexel.edu/~constant/work/agnclustering.ps for high resolution version. Accepted to Ap