Instantons from Blow-up

Abstract

We generalize Nakajima-Yoshioka blowup equations to arbitrary gauge group with hypermultiplets in arbitrary representations. Using our blowup equations, we compute the instanton partition functions for 4d N=2 and 5d N=1 gauge theories for arbitrary gauge theory with a large class of matter representations, without knowing explicit construction of the instanton moduli space. Our examples include exceptional gauge theories with fundamentals, SO(N) gauge theories with spinors, and SU(6) gauge theories with rank-3 antisymmetric hypers. Remarkably, the instanton partition function is completely determined by the perturbative part.

35+15 pages, 3 figures, v2: references added, minor corrections

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• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• Quantum toroidal algebras and solvable structures in gauge/string theory
• AdS${}_6$/CFT${}_5$ with O7-planes
• 5d/6d Wilson loops from blowups
• Instanton counting and O-vertex
• More on topological vertex formalism for 5-brane webs with O5-plane
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• BPS quivers of five-dimensional SCFTs, Topological Strings and q-Painlevé equations
• Instantons to the people: the power of one-form symmetries
• Twisted 6d $(2,0)$ SCFTs on a Circle
• Topological strings and Wilson loops
• Refined topological vertex with ON-planes
• 6d/5d exceptional gauge theories from web diagrams
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• ABCD of 't Hooft operators
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• $t{t}^{\ast }$ Toda equations for surface defects in $\mathcal{N}=2$ SYM and instanton counting for classical Lie groups
• Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries
• Bootstrapping ADE M-strings