Quiver varieties and Kac-Moody algebras

An Approach to Script N = 4 ADE Gauge Theory onK3

“…where q := exp(2πiτ ), and C G is Cartan Matrix of G. Notice that the above result is compatible with the result of Nakajima [19], that asserts that direct sum of the cohomology of the moduli space of U (1) instantons on ALE(G) is decomposed into level 1 representations of the affine Lie algebra of G. Combining (3.1) and (3.3), we estimate (at least as the first approximation) that the partition function Z K3 G (τ ) of N = 4 G Yang-Mills theory on K3 surface has the following form:…”

“…Fortunately, we already have the works on ADE blow-up formulas [24,19,9], which states that principal part of ADE blow-up formulas have the form of ADE theta functions θ A,D,E (τ ). In this paper, we proceed further and assert that the partition function of ADE gauge theory should take the form of (θ ADE (τ )/η(τ ) r+1 ) 24 (r is the rank of the gauge group).…”

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

“…In [101] we shall discuss the modification of the ADHM construction [8] producing the moduli spaces M γ (n, k) (cf. [77,88]) and the obstruction sheaf. More precisely, there is a moduli space of solutions to a system of matrix equations, determined by the quiver data, which depends on the choice of the Fayet-Illiopoulos (stability) parameters ζ ∈ R Vertγ .…”

Moduli of ADHM sheaves and the local Donaldson–Thomas theory

“…In particular the moduli space of supersymmetric flat directions of such configurations have been shown in [27] to be isomorphic to the quiver varieties constructed in [48,59]. These are moduli spaces of supersymmetric constant field configurations on the Dp-brane world-volume.…”