Multi-Caloron solutions

We discuss the construction of multi-caloron solutions with non-trivial holonomy, both as approximate superpositions and exact self-dual solutions. The charge k SU(n) moduli space can be described by kn constituent monopoles. Exact solutions help us to understand how these constituents can be seen as independent objects, which seems not possible with the approximate superposition. An "impurity scattering" calculation provides relatively simple expressions. Like at zero temperature an explicit parametrization requires solving a quadratic ADHM constraint, achieved here for a class of axially symmetric solutions. We will discuss the properties of these exact solutions in detail, but also demonstrate that interesting results can be obtained without explicitly solving for the constraint.Comment: 31 pages, 7 figures (in 19 parts

On How to Extend the NIR Tully-Fisher Relation to be Truly All-Sky

Dust extinction and stellar confusion by the Milky Way reduce the efficiency of detecting galaxies at low Galactic latitudes, creating the so-called Zone of Avoidance. This stands as a stumbling block in charting the distribution of galaxies and cosmic flow fields, and therewith our understanding of the local dynamics in the Universe (CMB dipole, convergence radius of bulk flows). For instance, ZoA galaxies are generally excluded from the whole-sky Tully-Fisher Surveys ($|b| \leq 5^\circ$) even if catalogued. We show here that by fine-tuning the near-infrared TF relation, there is no reason not to extend peculiar velocity surveys deeper into the ZoA. Accurate axial ratios ($b/a$) are crucial to both the TF sample selection and the resulting TF distances. We simulate the effect of dust extinction on the geometrical properties of galaxies. As expected, galaxies appear rounder with increasing obscuration level, even affecting existing TF samples. We derive correction models and demonstrate that we can reliably reproduce the intrinsic axial ratio from the observed value up to extinction level of about $A_J\simeq3$ mag ($A_V\sim11$ mag), we also recover a fair fraction of galaxies that otherwise would fall out of an uncorrected inclination limited galaxy sample. We present a re-calibration of the 2MTF relation in the NIR $J$, $H$, and $K_s$-bands for isophotal rather than total magnitudes, using their same calibration sample. Both TF relations exhibit similar scatter at high Galactic latitudes. However, the isophotal TF relation results in a significant improvement in the scatter for galaxies in the ZoA, and low surface brightness galaxies in general, because isophotal apertures are more robust in the face of significant stellar confusion.Comment: 12 pages, 10 figures, 4 tables, accepted for publication in MNRA

Galaxy peculiar velocities in the Zone of Avoidance

Dust extinction and stellar confusion of the Milky Way hinder the detection of galaxies at low Galactic latitude, creating the so-called Zone of Avoidance (ZoA). This has hampered our understanding of the local dynamics, cosmic flow fields and the origin of the Cosmic Microwave Background dipole. The ZoA ($|b| \le 5^\circ$) is also excluded from the "whole-sky" Two Micron All-Sky Survey (2MASS) Redshift Survey (2MRS) and 2MASS Tully-Fisher Survey (2MTF). The latter aims to provide distances and peculiar velocities for all bright inclined 2MASS galaxies with $K_s^o$ \leq 11\hbox{.\!\!^{\rm m}}25. Correspondingly, knowledge about the density distribution in the ZoA remains limited to statistical interpolations. To improve on this bias we pursued two different surveys to fill in the southern and northern ZoA. These data will allow a direct measurement of galaxy peculiar velocities. In this paper we will present a newly derived optimized Tully-Fisher (TF) relation that allow accurate measures of galaxy distances and peculiar velocities for dust-obscured galaxies. We discuss further corrections for magnitudes and biases and present some preliminary results on flow fields in the southern ZoA.Comment: 6 pages, 3 figures, to appear in Proceedings of SAIP2013, the 58th Annual Conference of the South African Institute of Physics, edited by Roelf Botha and Thulani Jili (SAIP and University of Zululand, 2014). ISBN: 978-0-620-62819-

On Nahm's transformation with twisted boundary conditions

Following two different tracks, we arrive at a definition of Nahm's transformation valid for self-dual fields on the 4-dimensional torus with non-zero twist tensor.The transform is again a self-dual gauge field defined on a new torus and with non-zero twist tensor. It preserves the property of being an involution.Comment: 18 page

HI Bright Galaxies in the Southern Zone of Avoidance

A blind survey for HI bright galaxies in the southern Zone of Avoidance, (212 deg < l < 36 deg; |b| < 5 deg), has been made with the 21 cm multibeam receiver on the Parkes 64 m radiotelescope. The survey, sensitive to normal spiral galaxies to a distance of about 40 Mpc and more nearby dwarfs, detected 110 galaxies. Of these, 67 have no counterparts in the NASA/IPAC Extragalactic Database. In general, the uncataloged galaxies lie behind thicker obscuration than do the cataloged objects. All of the newly-discovered galaxies have HI flux integrals more than an order of magnitude lower than the Circinus galaxy. The survey recovers the Puppis cluster and foreground group (Kraan-Korteweg & Huchtmeier 1992), and the Local Void remains empty. The HI mass function derived for the sample is satisfactorily fit by a Schechter function with parameters alpha = 1.51 +- 0.12, Phi* = 0.006 +- 0.003, and log M* = 9.7 +- 0.10.Comment: To appear in The Astronomical Journa

Constituent monopoles through the eyes of fermion zero-modes

We use the fermion zero-modes in the background of multi-caloron solutions with non-trivial holonomy as a probe for constituent monopoles. We find in general indication for an extended structure. However, for well separated constituents these become point-like. We analyse this in detail for the SU(2) charge 2 case, where one is able to solve the relevant Nahm equation exactly, beyond the piecewize constant solutions studied previously. Remarkably the zero-mode density can be expressed in the high temperature limit as a function of the conserved quantities that classify the solutions of the Nahm equation.Comment: 35 pages, 9 figures (in 26 parts

Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory

We analyze the zero-modes of the Dirac operator in quenched SU(3) gauge configurations at non-zero temperature and compare periodic and anti-periodic temporal boundary conditions for the fermions. It is demonstrated that for the different boundary conditions often the modes are localized at different space-time points and have different sizes. Our observations are consistent with patterns expected for Kraan - van Baal solutions of the classical Yang-Mills equations. These solutions consist of constituent monopoles and the zero-modes are localized on different constituents for different boundary conditions. Our findings indicate that the excitations of the QCD vacuum are more structured than simple instanton-like lumps.Comment: Remarks added. To appear in Phys. Rev.

Counting Yang-Mills Dyons with Index Theorems

We count the supersymmetric bound states of many distinct BPS monopoles in N=4 Yang-Mills theories and in pure N=2 Yang-Mills theories. The novelty here is that we work in generic Coulombic vacua where more than one adjoint Higgs fields are turned on. The number of purely magnetic bound states is again found to be consistent with the electromagnetic duality of the N=4 SU(n) theory, as expected. We also count dyons of generic electric charges, which correspond to 1/4 BPS dyons in N=4 theories and 1/2 BPS dyons in N=2 theories. Surprisingly, the degeneracy of dyons is typically much larger than would be accounted for by a single supermultiplet of appropriate angular momentum, implying many supermutiplets of the same charge and the same mass.Comment: 34 pages, 1 figure, LaTe

Topology and confinement

These lectures contain an introduction to instantons, calorons and dyons of the Yang--Mills gauge theory. Since we are interested in the mechanism of confinement and of the deconfinement phase transition at some critical temperature, the Yang--Mills theory is formulated and studied at nonzero temperatures. We introduce ``calorons with a nontrivial holonomy'' that are generalizations of instantons and can be viewed as ``made of'' constituent dyons. The quantum weight with which these calorons contribute to the Yang--Mills partition function is considered, and the ensuing statistical mechanics of the ensemble of interacting dyons is discussed. We argue that a simple semiclassical picture based on dyons satisfies all known criteria of confinement and explains the confinement-deconfinement phase transition. This refers not only to the SU(N) gauge groups where dyons lead to the expected behaviour of the observables with N, but also to the exceptional G(2) group whose group center, unlike SU(N), is trivial. Despite being centerless, the G(2) gauge group possesses confinement at low temperatures, and a 1st order deconfinement transition, according to several latest lattice simulations, indicating that confinement-deconfinement is not related to the group center. Dyons, however, reproduce this behaviour.Comment: Lectures at the ITEP Winter School (February 2009, Moscow) and Schladming Winter School (March 2009, Schladming, Austria), 42 pages, 16 figure