@article {2014,
title = {Vortex Partition Functions, Wall Crossing and Equivariant Gromov{\textendash}Witten Invariants},
number = {Communications in mathematical physics;volume 333; issue 2; pages 717-760;},
year = {2014},
publisher = {Springer},
abstract = {In this paper we identify the problem of equivariant vortex counting in a (2,2) supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov{\textendash}Witten invariants of the GIT quotient target space determined by the quiver. We provide new contour integral formulae for the I and J-functions encoding the equivariant quantum cohomology of the target space. Its chamber structure is shown to be encoded in the analytical properties of the integrand. This is explained both via general arguments and by checking several key cases. We show how several results in equivariant Gromov{\textendash}Witten theory follow just by deforming the integration contour. In particular, we apply our formalism to compute Gromov{\textendash}Witten invariants of the C3/Zn orbifold, of the Uhlembeck (partial) compactification of the moduli space of instantons on C2, and of An and Dn singularities both in the orbifold and resolved phases. Moreover, we analyse dualities of quantum cohomology rings of holomorphic vector bundles over Grassmannians, which are relevant to BPS Wilson loop algebrae.},
doi = {10.1007/s00220-014-2193-8},
url = {http://urania.sissa.it/xmlui/handle/1963/34652},
author = {Giulio Bonelli and Antonio Sciarappa and Alessandro Tanzini and Petr Vasko}
}
@article {2012,
title = {Vertices, vortices \& interacting surface operators},
journal = {JHEP 06(2012)178},
number = {SISSA;03/2011/FM-EP},
year = {2012},
note = {22 pages, 4 figures},
publisher = {SISSA},
abstract = {We show that the vortex moduli space in non-abelian supersymmetric N=(2,2) gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in four dimensions. The vortex partition functions for these theories are computed via equivariant localization. We show that these coincide with the field theory limit of the topological vertex on the strip with boundary conditions corresponding to column diagrams. Moreover, we resum the field theory limit of the vertex partition functions in terms of generalized hypergeometric functions formulating their AGT dual description as interacting surface operators of simple type. Analogously we resum the topological open string amplitudes in terms of q-deformed generalized hypergeometric functions proving that they satisfy appropriate finite difference equations.},
doi = {10.1007/JHEP06(2012)178},
url = {http://hdl.handle.net/1963/4134},
author = {Giulio Bonelli and Alessandro Tanzini and Zhao Jian}
}