Proposes comet-shaped quiver gauge theories for surface defects with nested instantons in 4D gauge theories on T^2 × T*C_{g,k} and gives conjectural explicit formulae for the virtual equivariant elliptic genus of bundles over nested Hilbert schemes of points on the affine plane.
Opers, surface defects, and Yang-Yang functional
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abstract
We explore the non-perturbative Dyson-Schwinger equations obeyed by the partition functions of the $\Omega$-deformed $\mathcal{N}=2, d=4$ supersymmetric linear quiver gauge theories in the presence of surface defects. We demonstrate that the partition functions of different types of defects (orbifold or vortex strings) are related by analytic continuation. We introduce Darboux coordinates on a patch of the moduli space of flat $SL(N)$-connections on a sphere with special punctures, which generalize the NRS coordinates defined in the $SL(2)$ case. Finally, we compare the generating function of the Lagrangian variety of opers in these Darboux coordinates with the effective twisted superpotential of the linear quiver theory in the two-dimensional $\Omega$-background, thereby proving the NRS conjecture and its generalization to the $SL(3)$ case.
fields
hep-th 3representative citing papers
Angular eigenvalues of the extreme charged C-metric are computed analytically via a confluent limit of SU(2)×SU(2) quiver gauge theory, matching numerical results.
Tropicalization of exact WKB formulae for NRS coordinates on the four-punctured sphere yields chamberwise agreement with Seiberg-Witten periods of SU(2) Nf=4 in unimodular primitive-symplectic chambers.
citing papers explorer
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Defects, nested instantons and comet shaped quivers
Proposes comet-shaped quiver gauge theories for surface defects with nested instantons in 4D gauge theories on T^2 × T*C_{g,k} and gives conjectural explicit formulae for the virtual equivariant elliptic genus of bundles over nested Hilbert schemes of points on the affine plane.
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Decoupling Limit of Quiver Theories and the Angular Spectra of Extreme C-metrics
Angular eigenvalues of the extreme charged C-metric are computed analytically via a confluent limit of SU(2)×SU(2) quiver gauge theory, matching numerical results.
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Tropical WKB asymptotics of NRS coordinates for opers in $SU(2)$, $N_f=4$ theory
Tropicalization of exact WKB formulae for NRS coordinates on the four-punctured sphere yields chamberwise agreement with Seiberg-Witten periods of SU(2) Nf=4 in unimodular primitive-symplectic chambers.