25 research outputs found
The Sen Limit
F-theory compactifications on elliptic Calabi-Yau manifolds may be related to
IIb compactifications by taking a certain limit in complex structure moduli
space, introduced by A. Sen. The limit has been characterized on the basis of
SL(2,Z) monodromies of the elliptic fibration. Instead, we introduce a stable
version of the Sen limit. In this picture the elliptic Calabi-Yau splits into
two pieces, a P^1-bundle and a conic bundle, and the intersection yields the
IIb space-time. We get a precise match between F-theory and perturbative type
IIb. The correspondence is holographic, in the sense that physical quantities
seemingly spread in the bulk of the F-theory Calabi-Yau may be rewritten as
expressions on the log boundary. Smoothing the F-theory Calabi-Yau corresponds
to summing up the D(-1)-instanton corrections to the IIb theory.Comment: 41 pp, 1 figure, LaTe
The Sen limit
F-theory compactifications on elliptic Calabi-Yau manifolds may be related to IIb compactifications by taking a certain limit in complex structure moduli space, introduced by A. Sen. The limit has been characterized on the basis of SL(2, Z) monodromies of the elliptic fibration. Instead, we introduce a stable version of the Sen limit. In this picture the elliptic Calabi-Yau splits into two pieces, a P -bundle and a conic bundle, and the intersection yields the IIb space-time. We get a precise match between F-theory and perturbative type IIb. The correspondence is holographic, in the sense that physical quantities seemingly spread in the bulk of the F-theory Calabi-Yau may be rewritten as expressions on the log boundary. Smoothing the F-theory Calabi-Yau corresponds to summing up the D(-1)-instanton corrections to the IIb theory.
The Geometry and Moduli of K3 Surfaces
These notes will give an introduction to the theory of K3 surfaces. We begin
with some general results on K3 surfaces, including the construction of their
moduli space and some of its properties. We then move on to focus on the theory
of polarized K3 surfaces, studying their moduli, degenerations and the
compactification problem. This theory is then further enhanced to a discussion
of lattice polarized K3 surfaces, which provide a rich source of explicit
examples, including a large class of lattice polarizations coming from elliptic
fibrations. Finally, we conclude by discussing the ample and Kahler cones of K3
surfaces, and give some of their applications.Comment: 34 pages, 2 figures. (R. Laza, M. Schutt and N. Yui, eds.
L-infinity algebra connections and applications to String- and Chern-Simons n-transport
We give a generalization of the notion of a Cartan-Ehresmann connection from
Lie algebras to L-infinity algebras and use it to study the obstruction theory
of lifts through higher String-like extensions of Lie algebras. We find
(generalized) Chern-Simons and BF-theory functionals this way and describe
aspects of their parallel transport and quantization.
It is known that over a D-brane the Kalb-Ramond background field of the
string restricts to a 2-bundle with connection (a gerbe) which can be seen as
the obstruction to lifting the PU(H)-bundle on the D-brane to a U(H)-bundle. We
discuss how this phenomenon generalizes from the ordinary central extension
U(1) -> U(H) -> PU(H) to higher categorical central extensions, like the
String-extension BU(1) -> String(G) -> G. Here the obstruction to the lift is a
3-bundle with connection (a 2-gerbe): the Chern-Simons 3-bundle classified by
the first Pontrjagin class. For G = Spin(n) this obstructs the existence of a
String-structure. We discuss how to describe this obstruction problem in terms
of Lie n-algebras and their corresponding categorified Cartan-Ehresmann
connections. Generalizations even beyond String-extensions are then
straightforward. For G = Spin(n) the next step is "Fivebrane structures" whose
existence is obstructed by certain generalized Chern-Simons 7-bundles
classified by the second Pontrjagin class.Comment: 100 pages, references and clarifications added; correction to section
5.1 and further example to 9.3.1 adde