The Stringy Instanton Partition Function

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.

30+1 pages;v2: references added;v3: added comments, version to appear in JHEP

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Cited by in corpus (17)

• Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants
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• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• A slow review of the AGT correspondence
• Supersymmetric localization in two dimensions
• A few Ricci-flat stacks as phases of exotic GLSM's
• ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• Blocks and Vortices in the 3d ADHM Quiver Gauge Theory
• Elliptic non-Abelian Donaldson-Thomas invariants of ${\mathbb{C}}^3$
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• The Condensate from Torus Knots
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• On Dimensional Transmutation in 1+1D Quantum Hydrodynamics
• Givental J-functions, Quantum integrable systems, AGT relation with surface operator
• Chiral rings for surface operators in 4d and 5d SQCD
• Stringy Instanton Counting and Topological Strings