Séminaire de Physique Théorique

# Surface defects and instanton-vortex moduli spaces

## by Prof. Bruno Le Floch (Princeton)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

### Amphithéâtre Léon Motchane

#### IHES

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

Instantons on R4, namely anti-self-dual Yang-Mills connections, are in bijection with framed locally free sheaves on CP2. Ramified instantons have an imposed singularity along R2 in R4 that translates to a parabolic structure along a CP1 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 R2, and gauging a global symmetry of the 2d theory using the R2 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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