Mathematics

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.