273 research outputs found
Self-Intersection Number of BPS Junctions in Backgrounds of Three and Seven-Branes
In a recent paper DeWolfe et al. have shown how to use the self-intersection
number of junctions to constrain the BPS spectrum of N=2, D=4 theories with ADE
flavor symmetry arising on a single D3-brane probe in a 7-brane background.
Motivated by the existence of more general N=2, D=4 theories arising on the
worldvolume of multiple D3-brane probes we show how to compute the
self-intersection number of junctions in the presence of 7-branes and multiple
D3-branes.Comment: 10 pages, Latex, 2 figure
Del Pezzo Surfaces and Affine 7-brane Backgrounds
A map between string junctions in the affine 7-brane backgrounds and vector
bundles on del Pezzo surfaces is constructed using mirror symmetry. It is shown
that the lattice of string junctions with support on an affine 7-brane
configuration is isomorphic to the K-theory group of the corresponding del
Pezzo surface. This isomorphism allows us to construct a map between the states
of the N=2, D=4 theories with E_N global symmetry realized in two different
ways in Type IIB and Type IIA string theory. A subgroup of the SL(2,Z) symmetry
of the \hat{E}_9 7-brane background appears as the Fourier-Mukai transform
acting on the D-brane configurations realizing vector bundles on elliptically
fibered B_9.Comment: 19 pages, LaTeX, 2 eps figures. v2: minor changes, version to appear
in JHE
Elliptic CY3folds and Non-Perturbative Modular Transformation
We study the refined topological string partition function of a class of
toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds
give rise to five dimensional quiver gauge theories and are dual to
configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for
these threefolds and show that the genus free energy is given by the weight
Eisenstein series. We also show that although the free energy at all
genera are modular invariant the full partition function satisfies the
non-perturbative modular transformation property discussed by Lockhart and Vafa
in arXiv:1210.5909 and therefore the modularity of free energy is up to
non-perturbative corrections.Comment: 12 page
M-strings, Elliptic Genera and N=4 String Amplitudes
We study mass-deformed N=2 gauge theories from various points of view. Their
partition functions can be computed via three dual approaches: firstly,
(p,q)-brane webs in type II string theory using Nekrasov's instanton calculus,
secondly, the (refined) topological string using the topological vertex
formalism and thirdly, M theory via the elliptic genus of certain M-strings
configurations. We argue for a large class of theories that these approaches
yield the same gauge theory partition function which we study in detail. To
make their modular properties more tangible, we consider a fourth approach by
connecting the partition function to the equivariant elliptic genus of R^4
through a (singular) theta-transform. This form appears naturally as a specific
class of one-loop scattering amplitudes in type II string theory on T^2, which
we calculate explicitly.Comment: 65 pages, a section on calculation of partition function using
Nekrasov's instanton calculus is adde
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