65 research outputs found
Instanton Counting and Chern-Simons Theory
The instanton partition function of N=2, D=4 SU(2) gauge theory is obtained
by taking the field theory limit of the topological open string partition
function, given by a Chern-Simons theory, of a CY3-fold. The CY3-fold on the
open string side is obtained by geometric transition from local F_0 which is
used in the geometric engineering of the SU(2) theory. The partition function
obtained from the Chern-Simons theory agrees with the closed topological string
partition function of local F_0 proposed recently by Nekrasov. We also obtain
the partition functions for local F_1 and F_2 CY3-folds and show that the
topological string amplitudes of all local Hirzebruch surfaces give rise to the
same field theory limit. It is shown that a generalization of the topological
closed string partition function whose field theory limit is the generalization
of the instanton partition function, proposed by Nekrasov, can be determined
easily from the Chern-Simons theory.Comment: 39 pages, references added, typos corrected, cosmetic change
The Acceleration of the Universe, a Challenge for String Theory
Recent astronomical observations indicate that the universe is accelerating.
We argue that generic quintessence models that accommodate the present day
acceleration tend to accelerate eternally. As a consequence the resulting
spacetimes exhibit event horizons. Hence, quintessence poses the same problems
for string theory as asymptotic de Sitter spaces.Comment: JHEP, LaTeX, 12 pages, 4 figures. Added a reference, corrected typo
The toroidal block and the genus expansion
We study the correspondence between four-dimensional supersymmetric gauge
theories and two-dimensional conformal field theories in the case of N=2* gauge
theory. We emphasize the genus expansion on the gauge theory side, as obtained
via geometric engineering from the topological string. This point of view
uncovers modular properties of the one-point conformal block on a torus with
complexified intermediate momenta: in the large intermediate weight limit, it
is a power series whose coefficients are quasi-modular forms. The all-genus
viewpoint that the conformal field theory approach lends to the topological
string yields insight into the analytic structure of the topological string
partition function in the field theory limit.Comment: 36 page
Moduli Potentials in Type IIA Compactifications with RR and NS Flux
We describe a simple class of type IIA string compactifications on Calabi-Yau
manifolds where background fluxes generate a potential for the complex
structure moduli, the dilaton, and the K\"ahler moduli. This class of models
corresponds to gauged N=2 supergravities, and the potential is completely
determined by a choice of gauging and by data of the N=2 Calabi-Yau model - the
prepotential for vector multiplets and the quaternionic metric on the
hypermultiplet moduli space. Using mirror symmetry, one can determine many
(though not all) of the quantum corrections which are relevant in these models.Comment: 30 pages, 2 figures; v2: minor change
The Vertex on a Strip
We demonstrate that for a broad class of local Calabi-Yau geometries built
around a string of IP^1's - those whose toric diagrams are given by
triangulations of a strip - we can derive simple rules, based on the
topological vertex, for obtaining expressions for the topological string
partition function in which the sums over Young tableaux have been performed.
By allowing non-trivial tableaux on the external legs of the corresponding web
diagrams, these strips can be used as building blocks for more general
geometries. As applications of our result, we study the behavior of topological
string amplitudes under flops, as well as check Nekrasov's conjecture in its
most general form.Comment: 26 pages, 12 figures; v2: minor corrections, version to appear in
ATM
Transformations of Spherical Blocks
We further explore the correspondence between N=2 supersymmetric SU(2) gauge
theory with four flavors on epsilon-deformed backgrounds and conformal field
theory, with an emphasis on the epsilon-expansion of the partition function
natural from a topological string theory point of view. Solving an appropriate
null vector decoupling equation in the semi-classical limit allows us to
express the instanton partition function as a series in quasi-modular forms of
the group Gamma(2), with the expected symmetry Weyl group of SO(8) semi-direct
S_3. In the presence of an elementary surface operator, this symmetry is
enhanced to an action of the affine Weyl group of SO(8) semi-direct S_4 on the
instanton partition function, as we demonstrate via the link between the null
vector decoupling equation and the quantum Painlev\'e VI equation.Comment: 31 pages, 1 figure; v2: typos corrected, references adde
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