On the Fermionic Frequencies of Circular Strings

We revisit the semiclassical computation of the fluctuation spectrum around different circular string solutions in AdS_5xS^5 and AdS_4xCP^3, starting from the Green-Schwarz action. It has been known that the results for these frequencies obtained from the algebraic curve and from the worldsheet computations sometimes do not agree. In particular, different methods give different results for the half-integer shifts in the mode numbers of the frequencies. We find that these discrepancies can be removed if one carefully takes into account the transition matrices in the spin bundle over the target space.Comment: 13 pages, 1 figur

Isogeometric preconditioners based on fast solvers for the Sylvester equation

We consider large linear systems arising from the isogeometric discretization of the Poisson problem on a single-patch domain. The numerical solution of such systems is considered a challenging task, particularly when the degree of the splines employed as basis functions is high. We consider a preconditioning strategy which is based on the solution of a Sylvester-like equation at each step of an iterative solver. We show that this strategy, which fully exploits the tensor structure that underlies isogeometric problems, is robust with respect to both mesh size and spline degree, although it may suffer from the presence of complicated geometry or coefficients. We consider two popular solvers for the Sylvester equation, a direct one and an iterative one, and we discuss in detail their implementation and efficiency for 2D and 3D problems on single-patch or conforming multi-patch NURBS geometries. Numerical experiments for problems with different domain geometries are presented, which demonstrate the potential of this approach