Superlocalization formulas and supersymmetric Yang–Mills theories

Abstract

By using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions.

Non-perturbative gauge/gravity correspondence in $ \mathcal{N} $ = 2 theories

“…The chiral correlators of the quiver gauge theory are given by insertions of χ 0I or χ 1J inside the instanton partition function. More precisely the correlators of the U(N 0 ) node are given by 15). A similar formula holds for tr N 1 e zΦ with the replacement O(z, χ 0I ) ↔ O(z, χ 1I ).…”

Multi-instanton calculus and equivariant cohomology

“…This is what we do here, by discussing the results that can be obtained from a proper supersymmetric formulation of the localization formulae for equivariant forms along the lines of [9]. Full details on this extension will appear elsewhere [23].…”

Stringy instanton effects in $ \mathcal{N} = 2 $ gauge theories

“…where the labels on the Pfaffian and determinants specify the representations on which Q 2 acts 8 , and neglected all numerical factors that are absorbed in the overall normalization. Thus, the k-instanton partition function is given in terms of the (super) determinant of Q 2 evaluated at the fixed points of Q in agreement with the localization formulas [38,53,54], and can be expressed in the following form…”