Higgs branch localization of 3d N = 2 theories

Abstract

We study N = 2 supersymmetric gauge theories on squashed 3-sphere and S 1 × S 2 . Recent studies have shown that the partition functions in a class of N = 2 theories have factorized forms in terms of vortex and anti-vortex partition functions by explicitly evaluating matrix integrals obtained from Coulomb branch localization. We directly derive this structure by performing Higgs branch localization. It turns out that more general N = 2 theories have this factorization property. We also discuss the factorization of supersymmetric Wilson

Factorisation and holomorphic blocks in 4d

“…Similarly to the 3d case, 4d holomorphic blocks are annihilated by a set of difference operators which can be interpreted as Ward identities for surface operators wrapping the torus T 2 σ and acting at the tip of the cigar. For example for B 4d D we find 12 27) where T q,x f (x) = f (qx) is the q-shift operator acting on x. The lens index is annihilated also by another equation for the tilde variables 28) and similarly for…”

Ellipsoid partition function from Seiberg-Witten monopoles

“…Such a Higgs branch localization computation was first performed in N = (2, 2) theories on the two-dimensional sphere [5,6], and later applied in and extended to two [7], three [41,42], four [43] and five [44] dimensional theories. 4 In this paper, we apply the Higgs branch localization technique to N = 2 supersymmetric theories placed on compact Euclidean manifolds.…”

Localisation on Sasaki-Einstein manifolds from holomorphic functions on the cone

“…Following the work of Pestun [4], the method has been applied to a large number of theories in two [5][6][7][8], three [9][10][11][12][13][14][15] four [16,17], and five dimensions, [18][19][20][21][22][23][24]. This development went hand-in-hand with an increased interest in theories with rigid supersymmetry on curved manifolds [25][26][27][28][29].…”