Radiation tails and boundary conditions for black hole evolutions

In numerical computations of Einstein's equations for black hole spacetimes, it will be necessary to use approximate boundary conditions at a finite distance from the holes. We point out here that ``tails,'' the inverse power-law decrease of late-time fields, cannot be expected for such computations. We present computational demonstrations and discussions of features of late-time behavior in an evolution with a boundary condition.Comment: submitted to Phys. Rev.

Wavy Wilson Line and AdS/CFT

Wilson loops which are small deviations from straight, infinite lines, called wavy lines, are considered in the context of the AdS/CFT correspondence. A single wavy line and the connected correlation function of a straight and wavy line are considered. It is argued that, to leading order in ``waviness'', the functional form of the loop is universal and the coefficient, which is a function of the 't Hooft coupling, is found in weak coupling perturbation theory and the strong coupling limit using the AdS/CFT correspondence. Supersymmetric arguments are used to simplify the computation and to show that the straight line obeys the Migdal-Makeenko loop equation

Exact results for static and radiative fields of a quark in N=4 super Yang-Mills

In this work (which supersedes our previous preprint arXiv:1112.2345) we determine the expectation value of the N=4$ SU(N) SYM Lagrangian density operator in the presence of an infinitely heavy static particle in the symmetric representation of SU(N), by means of a D3-brane probe computation. The result that we obtain coincides with two previous computations of different observables, up to kinematical factors. We argue that these agreements go beyond the D-brane probe approximation, which leads us to propose an exact formula for the expectation value of various operators. In particular, we provide an expression for the total energy loss by radiation of a heavy particle in the fundamental representation.Comment: 14 pages. This submission supersedes our previous preprint arXiv:1112.2345. v2: numerical factors fixed, minor clarifications, added reference

Effective string theory for vortex lines in fluids and superfluids

We discuss the effective string theory of vortex lines in ordinary fluids and low-temperature superfluids, by describing the bulk fluid flow in terms of a two-form field to which vortex lines can couple. We derive the most general low-energy effective Lagrangian that is compatible with (spontaneously broken) Poincare invariance and worldsheet reparameterization invariance. This generalizes the effective action developed by Lund and Regge and by Endlich and Nicolis. By applying standard field-theoretical techniques, we show that certain low-energy coupling constants -- most notably the string tension -- exhibit RG running already at the classical level. We discuss applications of our techniques to the study of Kelvin waves, vortex rings, and the coupling to bulk sound modes.Comment: 62 pages, 6 figure

Wilson loops in SYM theory: from weak to strong coupling

We review Wilson loops in N=4 supersymmetric Yang-Mills theory with emphasis on the exact results. The implications are discussed in the context of the AdS/CFT correspondence.Comment: 32 pages, 5 figure

Straight-line instruction sequence completeness for total calculation on cancellation meadows

A combination of program algebra with the theory of meadows is designed leading to a theory of computation in algebraic structures which use in addition to a zero test and copying instructions the instruction set $\{x \Leftarrow 0, x \Leftarrow 1, x\Leftarrow -x, x\Leftarrow x^{-1}, x\Leftarrow x+y, x\Leftarrow x\cdot y\}$. It is proven that total functions on cancellation meadows can be computed by straight-line programs using at most 5 auxiliary variables. A similar result is obtained for signed meadows.Comment: 24 page