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arXiv · 1306.0432

The Stringy Instanton Partition Function

Giulio Bonelli·Antonio Sciarappa·Alessandro Tanzini·Petr Vasko
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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.

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Giulio Bonelli, Antonio Sciarappa, Alessandro Tanzini, Petr Vasko. 2013-12-19. The Stringy Instanton Partition Function. https://doi.org/10.1007/jhep01(2014)038

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