6 research outputs found
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
Superconformal M2-branes and generalized Jordan triple systems
Three-dimensional conformal theories with six supersymmetries and SU(4)
R-symmetry describing stacks of M2-branes are here proposed to be related to
generalized Jordan triple systems. Writing the four-index structure constants
in an appropriate form, the Chern-Simons part of the action immediately
suggests a connection to such triple systems. In contrast to the previously
considered three-algebras, the additional structure of a generalized Jordan
triple system is associated to a graded Lie algebra, which corresponds to an
extension of the gauge group. In this note we show that the whole theory with
six manifest supersymmetries can be naturally expressed in terms of such a
graded Lie algebra. Also the BLG theory with eight supersymmetries is included
as a special case.Comment: 15 pages, v2 and v3: minor corrections and clarifications, references
added, v2: section 4 extended, v3: published versio
On the structure of k-Lie algebras
We show that the structure constants of -Lie algebras, , with a
positive definite metric are the sum of the volume forms of orthogonal
-planes. This generalizes the result for in arXiv:0804.2662 and
arXiv:0804.3078, and confirms a conjecture in math/0211170.Comment: 4 pages, minor changes and a reference adde