The partition bundle of type A_{N-1} (2, 0) theory

Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometric data (i.e. an orientation, a spin structure, a conformal structure, and an R-symmetry bundle with connection). We discuss the nature of the object that generalizes the partition function of a more conventional quantum theory. This object takes its values in a certain complex vector space, which fits together into the total space of a complex vector bundle (the `partition bundle') as the data on the six-manifold is varied in its infinite-dimensional parameter space. In this context, an important role is played by the middle-dimensional intermediate Jacobian of the six-manifold endowed with some additional data (i.e. a symplectic structure, a quadratic form, and a complex structure). We define a certain hermitian vector bundle over this finite-dimensional parameter space. The partition bundle is then given by the pullback of the latter bundle by the map from the parameter space related to the six-manifold to the parameter space related to the intermediate Jacobian.Comment: 15 pages. Minor changes, added reference

Rigid surface operators and S-duality: some proposals

We study surface operators in the N=4 supersymmetric Yang-Mills theories with gauge groups SO(n) and Sp(2n). As recently shown by Gukov and Witten these theories have a class of rigid surface operators which are expected to be related by S-duality. The rigid surface operators are of two types, unipotent and semisimple. We make explicit proposals for how the S-duality map should act on unipotent surface operators. We also discuss semisimple surface operators and make some proposals for certain subclasses of such operators.Comment: 27 pages. v2: minor changes, added referenc

Wave-growth associated with turbulent spot in plane Poiseuille flow

A kinematic wave theory is used to investigate the cause of the rapid growth of waves observed at the wingtip of turbulent spot in plane Poiseuille flow. It is found that the qualitative behavior of the wave motions is well described by Landahl's breakdown criterion as the wave selection procedure. The predicted wave number, wave angle, and phase velocity are in agreement with those values obtained in a direct simulation

Turbulence characteristics inside a turbulent spot in plane Poiseuille flow

In wall-bounded shear flows the transition to turbulence through localized disturbances goes through a pattern starting with a development of shear layers. The localized normal velocity fluctuations induce normal vorticity through the lift-up effect. These shear layers become unstable to secondary disturbances, and if the amplitudes of the disturbances are large enough, a turbulent spot develops. Investigations of the spot in boundary layers has shown that the turbulent part of the spot is very similar to a fully developed boundary layer. Wygnanski et al. (1976) showed that the mean profile at the center-symmetry plane has a logarithmic region and Johansson et al. (1987) showed that both the higher-order statistics and flow structures in the spot were the same as in the corresponding fully developed flow. In what respects the turbulence inside the Poiseuille spot is similar to fully developed turbulent channel flow is studied. The numerically simulated spot is used, where the characteristics inside the spot are compared to those of the wave packet in the wingtip area. A recent experimental investigation of the velocity field associated with the Poiseuille spot by Klingmann et al. is used for comparison

First Law, Counterterms and Kerr-AdS_5 Black Holes

We apply the counterterm subtraction technique to calculate the action and other quantities for the Kerr--AdS black hole in five dimensions using two boundary metrics; the Einstein universe and rotating Einstein universe with arbitrary angular velocity. In both cases, the resulting thermodynamic quantities satisfy the first law of thermodynamics. We point out that the reason for the violation of the first law in previous calculations is that the rotating Einstein universe, used as a boundary metric, was rotating with an angular velocity that depends on the black hole rotation parameter. Using a new coordinate system with a boundary metric that has an arbitrary angular velocity, one can show that the resulting physical quantities satisfy the first law.Comment: 19 pages, 1 figur

't Hooft Operators in the Boundary

We consider a topologically twisted maximally supersymmetric Yang-Mills theory on a four-manifold of the form $V = W \times {\mathbb R}_+$. 't Hooft disorder operators localized in the boundary component at finite distance of $V$ are relevant for the study of knot theory on the three-manifold $W$, and have recently been constructed for a gauge group of rank one. We extend this construction to an arbitrary gauge group $G$. For certain values of the magnetic charge of the 't Hooft operator, the solutions are obtained by embedding the rank one solutions in $G$ and can be given in closed form.Comment: 9 page

The Self-Dual String and Anomalies in the M5-brane

We study the anomalies of a charge $Q_2$ self-dual string solution in the Coulomb branch of $Q_5$ M5-branes. Cancellation of these anomalies allows us to determine the anomaly of the zero-modes on the self-dual string and their scaling with $Q_2$ and $Q_5$. The dimensional reduction of the five-brane anomalous couplings then lead to certain anomalous couplings for D-branes.Comment: 13 pages, Harvmac, refs adde

Large scale flow around turbulent spots

Numerical simulations of a model of plane Couette flow focusing on its in-plane spatio-temporal properties are used to study the dynamics of turbulent spots.Comment: 16 pages, 6 figure