Instantons to the people: the power of one-form symmetries

Abstract

We show that the non-perturbative dynamics of $\mathcal{N}=2$ super Yang-Mills theories in a self-dual $\Omega$-background and with an arbitrary simple gauge group is fully determined by studying renormalization group equations of vevs of surface operators generating one-form symmetries. The corresponding system of equations is a {\it non-autonomous} Toda chain, the time being the RG scale. We obtain new recurrence relations which provide a systematic algorithm computing multi-instanton corrections from the tree-level one-loop prepotential as the asymptotic boundary condition of the RGE. We exemplify by computing the $E_6$ and $G_2$ cases up to two-instantons.

two columns, 5 pages

References in corpus (4)

• Generalized Global Symmetries
• On determinant representation and integrability of Nekrasov functions
• Instantons from Blow-up
• Blowups in BPS/CFT correspondence, and Painlevé VI

Cited by in corpus (9)

• Exact solution of Kerr black hole perturbations via CFT${}_2$ and instanton counting. Greybody factor, Quasinormal modes and Love numbers
• Instanton counting and O-vertex
• ABCD of qq-characters
• M2-branes and $\mathfrak{q}$-Painlevé equations
• $t{t}^{\ast }$ Toda equations for surface defects in $\mathcal{N}=2$ SYM and instanton counting for classical Lie groups
• Five-dimensional gauge theories and the local B-model
• On a 5D UV completion of Argyres-Douglas theories
• Fredholm Pfaffian $\tau$-functions for orthogonal isospectral and isomonodromic systems
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations