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SUMMARY:Surface defects and instanton-vortex moduli spaces
DTSTART;VALUE=DATE-TIME:20171006T123000Z
DTEND;VALUE=DATE-TIME:20171006T133000Z
DTSTAMP;VALUE=DATE-TIME:20210417T104312Z
UID:indico-event-2812@indico.math.cnrs.fr
DESCRIPTION:Instantons on R4\, namely anti-self-dual Yang-Mills connection
s\, are in bijection with framed locally free sheaves on CP2. Ramified ins
tantons have an imposed singularity along R2 in R4 that translates to a pa
rabolic structure along a CP1 divisor\, or equivalently to a cyclic orbifo
ld. Such a singularity (Gukov-Witten defect) can be obtained in 4d N=2 s
upersymmetric Yang-Mills theory by adding 2d N=(2\,2) degrees of freedom o
n R2\, and gauging a global symmetry of the 2d theory using the R2 restric
tion of the 4d gauge connection. The moduli space of ramified instantons
should thus be related to a moduli space of instanton-vortex configuratio
ns of the 4d-2d pair of gauge theories. I propose an incomplete definiti
on 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 Hig
gs branch stack. As evidence I compare Nekrasov partition functions\, na
mely 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.\n\nhttps://indico.math.cnrs.fr
/event/2812/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/2812/
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