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Title:
Twisted indices of 3d supersymmetric gauge theories and moduli spaces of vortices
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Abstract:
I discuss the geometric interpretation of the twisted index of 3d supersymmetric gauge theories on a closed Riemann surface. I show that the twisted index reproduces the virtual Euler characteristic of the moduli space of solutions to vortex equations on the Riemann surface. I also discuss 3d N = 4 mirror symmetry in this context, which implies non-trivial relations between enumerative invariants associated to the moduli space of vortices. Finally, I discuss a wall-crossing formula of the twisted indices derived from the gauge theory point of view.
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