Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensions

We investigate strong-to-weak coupling transitions in D=2+1 SU(N->oo) gauge theories, by simulating lattice theories with a Wilson plaquette action. We find that there is a strong-to-weak coupling cross-over in the lattice theory that appears to become a third-order phase transition at N=oo, in a manner that is essentially identical to the Gross-Witten transition in the D=1+1 SU(oo) lattice gauge theory. There is also evidence for a second order transition at N=oo at approximately the same coupling, which is connected with centre monopoles (instantons) and so analogues to the first order bulk transition that occurs in D=3+1 lattice gauge theories for N>4. We show that as the lattice spacing is reduced, the N=oo gauge theory on a finite 3-torus suffers a sequence of (apparently) first-order ZN symmetry breaking transitions associated with each of the tori (ordered by size). We discuss how these transitions can be understood in terms of a sequence of deconfining transitions on ever-more dimensionally reduced gauge theories.We investigate whether the trace of the Wilson loop has a non-analyticity in the coupling at some critical area, but find no evidence for this although, just as in D=1+1,the eigenvalue density of a Wilson loop forms a gap at N=oo for a critical trace. The physical implications of this are unclear.The gap formation is a special case of a remarkable similarity between the eigenvalue spectra of Wilson loops in D=1+1 and D=2+1 (and indeed D=3+1): for the same value of the trace, the eigenvalue spectra are nearly identical.This holds for finite as well as infinite N; irrespective of the Wilson loop size in lattice units; and for Polyakov as well as Wilson loops.Comment: 44 pages, 28 figures. Extensive changes and clarifications with new results on non-analyticities and eigenvalue spectra of Wilson loops. This version to be submitted for publicatio

Testing wind as an explanation for the spin problem in the continuum-fitting method

The continuum-fitting method is one of the two most advanced methods of determining the black hole spin in accreting X-ray binary systems. There are, however, still some unresolved issues with the underlying disk models. One of them manifests as an apparent decrease in spin for increasing source luminosity. Here, we perform a few simple tests to establish whether outflows from the disk close to the inner radius can address this problem. We employ four different parametric models to describe the wind and compare these to the apparent decrease in spin with luminosity measured in the sources LMC~X-3 and GRS~1915+105. Wind models in which parameters do not explicitly depend on the accretion rate cannot reproduce the spin measurements. Models with mass accretion rate dependent outflows, however, have spectra that emulate the observed ones. The assumption of a wind thus effectively removes the artifact of spin decrease. This solution is not unique; the same conclusion can be obtained with a truncated inner disk model. To distinguish among valid models, high resolution X-ray data and a realistic description of the Comptonization in the wind will be needed.Comment: 14 pages, 11 figures, accepted by Ap

Infinite N phase transitions in continuum Wilson loop operators

We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character as unitary matrices and undergo a phase transition at infinite N reflected by the eigenvalue distribution closing a gap in its spectrum when the defining smooth loop is dilated from a small size to a large one. If this large N phase transition belongs to a solvable universality class one might be able to calculate analytically the string tension in terms of the perturbative Lambda-parameter. This would be achieved by matching instanton results for small loops to the relevant large-N-universal function which, in turn, would be matched for large loops to an effective string theory. Similarities between our findings and known analytical results in two dimensional space-time indicate that the phase transitions we found only affect the eigenvalue distribution, but the traces of finite powers of the Wilson loop operators stay smooth under scaling.Comment: 31 pages, 9 figures, typos and references corrected, minor clarifications adde

A theoretical study of the time-lags due to Comptonization and the constraints on the X-ray corona in AGN

We study the Fourier time-lags due to the Comptonization of disc-emitted photons in a spherical, uniform, and stationary X-ray corona, which located on the rotational axis of the black hole. We use Monk, a general relativistic Monte-Carlo radiative transfer code, to calculate Compton scattering of photons emitted by a thin disc with a Novikov-Thorne temperature profile. We find that the model time-lags due to Comptonization remain constant up to a characteristic frequency and then rapidly decrease to zero at higher frequencies. We provide equations which can be used to determine the time-lags and cross spectra for a wide range of values for the corona radius, temperature, optical depth, height, and for various accretion rates and black hole masses. We also provide an equation for the X-ray luminosity of a single corona, as a function of the its characteristics and location above the disc. Remarkably, the observed X-ray time-lags of nearby, bright active galaxies can be successfully reproduced by inverse Comptonization process of multiple dynamic coronae.Comment: 16 pages, 17 figures; accepted for publication in MNRA

Vertical dissipation profiles and the photosphere location in thin and slim accretion disks

We calculate optically thick but geometrically thin (and slim) accretion disk models and perform a ray-tracing of photons (in the Kerr geometry) to calculate the observed disk spectra. Previously, it was a common practice to ray-trace photons assuming that they are emitted from the Kerr geometry equatorial plane, z = 0. We show that the spectra calculated with this assumption differ from these calculated under the assumption that photons are emitted from the actual surface of the disc, z = H(r). This implies that a knowledge of the location of the thin disks effective photosphere is relevant for calculating the spectra. In this paper we investigate, in terms of a simple toy model, a possible influence of the (unknown, and therefore ad hoc assumed) vertical dissipation profiles on the vertical structure of the disk and thus on the location of the effective photosphere, and on the observed spectra. For disks with moderate and high mass accretion rates (\dot m>0.01\dot m_C) we find that the photosphere location in the inner, radiation pressure dominated, disk region (where most of the radiation comes from) does not depend on the dissipation profile and therefore emerging disk spectra are insensitive to the choice of the dissipation function. For lower accretion rates the photosphere location depends on the assumed vertical dissipation profile down to the disk inner edge, but the dependence is very weak and thus of minor importance. We conclude that the spectra of optically thick accretion disks around black holes should be calculated with the ray-tracing from the effective photosphere and that, fortunately, the choice of a particular vertical dissipation profile does not substantially influence the calculated spectrum.Comment: 7 pages, 7 figure

SO(2N) and SU(N) gauge theories in 2+1 dimensions

We perform an exploratory investigation of how rapidly the physics of SO(2N) gauge theories approaches its N=oo limit. This question has recently become topical because SO(2N) gauge theories are orbifold equivalent to SU(N) gauge theories, but do not have a finite chemical potential sign problem. We consider only the pure gauge theory and, because of the inconvenient location of the lattice strong-to-weak coupling 'bulk' transition in 3+1 dimensions, we largely confine our numerical calculations to 2+1 dimensions. We discuss analytic expectations in both D=2+1 and D=3+1, show that the SO(6) and SU(4) spectra do indeed appear to be the same, and show that a number of mass ratios do indeed appear to agree in the large-N limit. In particular SO(6) and SU(3) gauge theories are quite similar except for the values of the string tension and coupling, both of which differences can be readily understood.Comment: 27 pages, 9 figure