4 research outputs found
The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories
We analyse the fluctuations of the ground-state/funnel solutions proposed to
describe M2-M5 systems in the level-k mass-deformed/pure Chern-Simons-matter
ABJM theory of multiple membranes. We show that in the large N limit the
fluctuations approach the space of functions on the 2-sphere rather than the
naively expected 3-sphere. This is a novel realisation of the fuzzy 2-sphere in
the context of Matrix Theories, which uses bifundamental instead of adjoint
scalars. Starting from the multiple M2-brane action, a U(1) Yang-Mills theory
on R^{2,1} x S^2 is recovered at large N, which is consistent with a single
D4-brane interpretation in Type IIA string theory. This is as expected at large
k, where the semiclassical analysis is valid. Several aspects of the
fluctuation analysis, the ground-state/funnel solutions and the
mass-deformed/pure ABJM equations can be understood in terms of a discrete
noncommutative realisation of the Hopf fibration. We discuss the implications
for the possibility of finding an M2-brane worldvolume derivation of the
classical S^3 geometry of the M2-M5 system. Using a rewriting of the equations
of the SO(4)-covariant fuzzy 3-sphere construction, we also directly compare
this fuzzy 3-sphere against the ABJM ground-state/funnel solutions and show
them to be different.Comment: 60 pages, Latex; v2: references added; v3: typos corrected and
references adde
The guns of Travancore or how much powder may a Maharaja blow away?
The main focus of this article is the chequered history of Travancore state's gun salutes. After the somewhat unexpected award of a prestigious dynastic salute in 1866, all later efforts to rise in the hierarchy of guns remained in vain. What were the grounds on which gun salutes were claimed by the rulers of Travancore, and granted or withheld by the British-Indian government? A related question is the paucity of documentary evidence that both parties had to cope with. What kind of knowledge did both parties actually posses when invoking the sanction of immemorial custom in support of their claims