Séminaire de Physique Théorique
# Surface defects and instanton-vortex moduli spaces

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Europe/Paris

Amphithéâtre Léon Motchane (IHES)
### Amphithéâtre Léon Motchane

#### IHES

35, route de Chartres, F-91440 Bures-sur-Yvette (France)

Description

Instantons on R^{4}, namely anti-self-dual Yang-Mills connections, are in bijection with framed locally free sheaves on CP^{2}. Ramified instantons have an imposed singularity along R^{2} in R^{4} that translates to a parabolic structure along a CP^{1} divisor, or equivalently to a cyclic orbifold. Such a singularity (Gukov-Witten defect) can be obtained in 4d N=2 supersymmetric Yang-Mills theory by adding 2d N=(2,2) degrees of freedom on R^{2}, and gauging a global symmetry of the 2d theory using the R^{2} restriction of the 4d gauge connection. The moduli space of ramified instantons should thus be related to a moduli space of instanton-vortex configurations of the 4d-2d pair of gauge theories. I propose an incomplete definition of the latter moduli space by fibering (over the instanton moduli space) a recent description of the vortex moduli space as based maps to the Higgs branch stack. As evidence I compare Nekrasov partition functions, namely equivariant integrals over these moduli spaces. The equality relies on Jeffrey-Kirwan technology, applicable thanks to the ADHM construction of the moduli spaces as Kähler quotients.

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