Mathew Bullimore, Andrea E.V. Ferrari, Heeyeon Kim
SciPost Phys. 12, 186 (2022) ·
published 8 June 2022
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We study the twisted index of 3d $\mathcal{N}=2$ supersymmetric gauge theories on $S^1 \times \Sigma$ in the presence of a real FI parameter deformation. This parameter induces a 1d FI parameter for the effective supersymmetric quantum mechanics on $S^1$. Using supersymmetric localisation, the twisted index can be expressed as a contour integral. We show that the contour prescription is modified in the presence of the 1d FI parameter, leading to wall-crossing phenomena for the twisted index. In particular, we derive a general wall-crossing formula for abelian gauge theories. We also examine the origin of wall-crossing as change of stability condition in the algebro-geometric interpretation of the twisted index. These ideas are illustrated for abelian theories with $\mathcal{N}=4$ supersymmetry and in a non-abelian example that reproduces wall-crossing phenomena associated to moduli spaces of stable pairs.
SciPost Phys. 12, 072 (2022) ·
published 23 February 2022
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This paper studies supersymmetric ground states of 3d $\mathcal{N}=4$
supersymmetric gauge theories on a Riemann surface of genus $g$. There are two
distinct spaces of supersymmetric ground states arising from the $A$ and $B$
type twists on the Riemann surface, which lead to effective supersymmetric
quantum mechanics with four supercharges and supermultiplets of type
$\mathcal{N}=(2,2)$ and $\mathcal{N}=(0,4)$ respectively. We compute the space
of supersymmetric ground states in each case, graded by flavour and
R-symmetries and in different chambers for real mass and FI parameters, for a
large class of supersymmetric gauge theories. The results are formulated
geometrically in terms of the Higgs branch geometry. We perform extensive
checks of compatibility with the twisted index and mirror symmetry.
Prof. Kim: "The authors would like to than..."
in Submissions | report on Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface