1,438 research outputs found
A symplectic dynamics proof of the degree-genus formula
We classify global surfaces of section for the Reeb flow of the standard
contact form on the 3-sphere, defining the Hopf fibration. As an application,
we prove the degree-genus formula for complex projective curves, using an
elementary degeneration process inspired by the language of holomorphic
buildings in symplectic field theory.Comment: 24 pages, 11 figure
Correlators of Hopf Wilson loops in the AdS/CFT correspondence
We study at quantum level correlators of supersymmetric Wilson loops with
contours lying on Hopf fibers of . In SYM theory the
strong coupling analysis can be performed using the AdS/CFT correspondence and
a connected classical string surface, linking two different fibers, is
presented. More precisely, the string solution describes oppositely oriented
fibers with the same scalar coupling and depends on an angular parameter,
interpolating between a non-BPS configuration and a BPS one. The system can be
thought as an alternative deformation of the ordinary antiparallel lines giving
the static quark-antiquark potential, that is indeed correctly reproduced, at
weak and strong coupling, as the fibers approach one another.Comment: 38 pages, 5 figure
Dynamics of Toroidal Spiral Strings around Five-dimensional Black Holes
We examine the separability of the Nambu-Goto equation for test strings in a
shape of toroidal spiral in a five-dimensional Kerr-AdS black hole. In
particular, for a `{\it Hopf loop}\rq string which is a special class of the
toroidal spiral strings, we show the complete separation of variables occurs in
two cases, Kerr background and Kerr-AdS background with equal angular momenta.
We also obtain the dynamical solution for the Hopf loop around a black hole and
for the general toroidal spiral in Minkowski background.Comment: 16 pages, 1 figure, minor changes, references adde
Transversely holomorphic flows and contact circles on spherical 3-manifolds
Motivated by the moduli theory of taut contact circles on spherical
3-manifolds, we relate taut contact circles to transversely holomorphic flows.
We give an elementary survey of such 1-dimensional foliations from a
topological viewpoint. We describe a complex analogue of the classical
Godbillon-Vey invariant, the so-called Bott invariant, and a logarithmic
monodromy of closed leaves. The Bott invariant allows us to formulate a
generalised Gau{\ss}-Bonnet theorem. We compute these invariants for the
Poincar\'e foliations on the 3-sphere and derive rigidity statements, including
a uniformisation theorem for orbifolds. These results are then applied to the
classification of taut contact circles.Comment: 31 pages, 3 figures; v2: changes to the exposition, additional
reference
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