We show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between $\mathcal{N}=2$\ supersymmetric gauge theories and two-dimensional conformal field theory. Talk presented by A.T. at the conference Interactions between Geometry and Physics {\textemdash} in honor of Ugo Bruzzo{\textquoteright}s 60th birthday 17{\textendash}22 August 2015, Guaruj{\'a}, S{\~a}o Paulo, Brazil, mostly based on Bawane et al. (0000) and Bershtein et al. (0000).

}, keywords = {AGT, Donaldson invariants, Equivariant localization, Exact partition function, Supersymmetry, Virasoro conformal blocks}, issn = {0393-0440}, doi = {https://doi.org/10.1016/j.geomphys.2017.01.012}, url = {http://www.sciencedirect.com/science/article/pii/S0393044017300165}, author = {Mikhail Bershtein and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {2012, title = {Gauge Theories on ALE Space and Super Liouville Correlation Functions}, journal = {Lett. Math. Phys. 101 (2012) 103-124}, number = {arXiv:1107.4609v1;}, year = {2012}, note = {21 pages}, publisher = {SISSA}, abstract = {We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the N=2^* instanton partition function is given by the product of the character of \\\\hat{SU}(2)_2 times the super Virasoro conformal block on the torus with one puncture.}, doi = {10.1007/s11005-012-0553-x}, url = {http://hdl.handle.net/1963/4305}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini} } @article {2011, title = {Generalized matrix models and AGT correspondence at all genera}, journal = {JHEP, Volume 2011, Issue 7, 2011, Article number055}, number = {arXiv:1011.5417;}, year = {2011}, note = {This version is published in : Journal of High Energy Physics, Volume 2011, Issue 7, 2011, Article number055}, publisher = {SISSA}, abstract = {We study generalized matrix models corresponding to n-point Virasoro\r\nconformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT\r\ncorrespondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge\r\ntheories with generalized quiver diagrams. We obtain the generalized matrix\r\nmodels from the perturbative evaluation of the Liouville correlation functions\r\nand verify the consistency of the description with respect to degenerations of\r\nthe Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2\r\ngauge theory as the spectral curve of the generalized matrix model, thus\r\nproviding a check of AGT correspondence at all genera.}, doi = {10.1007/JHEP07(2011)055}, url = {http://hdl.handle.net/1963/6568}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini and Futoshi Yagib} }