@article {2014,
title = {Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics},
number = {Journal of high energy physics;volume 2014; issue 7; article number 141;},
year = {2014},
publisher = {Springer},
abstract = {We show that the exact partition function of U(N) six-dimensional gauge
theory with eight supercharges on C^2 x S^2 provides the quantization of the
integrable system of hydrodynamic type known as gl(N) periodic Intermediate
Long Wave (ILW). We characterize this system as the hydrodynamic limit of
elliptic Calogero-Moser integrable system. We compute the Bethe equations from
the effective gauged linear sigma model on S^2 with target space the ADHM
instanton moduli space, whose mirror computes the Yang-Yang function of gl(N)
ILW. The quantum Hamiltonians are given by the local chiral ring observables of
the six-dimensional gauge theory. As particular cases, these provide the gl(N)
Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four
dimensional limit, we identify the local chiral ring observables with the
conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge
theoretical proof of AGT correspondence.},
doi = {10.1007/JHEP07(2014)141},
url = {http://urania.sissa.it/xmlui/handle/1963/34546},
author = {Giulio Bonelli and Antonio Sciarappa and Alessandro Tanzini and Petr Vasko}
}
@article {2014,
title = {The stringy instanton partition function},
number = {Journal of high energy physics;volume 2014; issue 1; article number 038;},
year = {2014},
publisher = {Springer},
abstract = {We perform an exact computation of the gauged linear sigma model associated
to a D1-D5 brane system on a resolved A_1 singularity. This is accomplished via
supersymmetric localization on the blown-up two-sphere. We show that in the
blow-down limit C^2/Z_2 the partition function reduces to the Nekrasov
partition function evaluating the equivariant volume of the instanton moduli
space. For finite radius we obtain a tower of world-sheet instanton
corrections, that we identify with the equivariant Gromov-Witten invariants of
the ADHM moduli space. We show that these corrections can be encoded in a
deformation of the Seiberg-Witten prepotential. From the mathematical
viewpoint, the D1-D5 system under study displays a twofold nature: the
D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM
instanton moduli space in the Givental formalism, and the D5-branes viewpoint
is related to higher rank equivariant Donaldson-Thomas invariants of P^1 x C^2.},
doi = {10.1007/JHEP01(2014)038},
url = {http://urania.sissa.it/xmlui/handle/1963/34589},
author = {Giulio Bonelli and Antonio Sciarappa and Alessandro Tanzini and Petr Vasko}
}