Darboux Coordinates and Instanton Corrections in Projective Superspace

Abstract

By demanding consistency of the Legendre transform construction of hyperkähler metrics in projective superspace, we derive the expression for the Darboux coordinates on the hyperkähler manifold. We apply these results to study the Coulomb branch moduli space of 4D, N=2 super-Yang-Mills theory (SYM) on R^3 x S^1, recovering the results by GMN. We also apply this method to study the electric corrections to the moduli space of 5D, N=1 SYM on R^3 x T^2 and give the Darboux coordinates explicitly.

22 pages; more references added, typos corrected and minor modifications in v3

References in corpus (4)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• D-instantons and twistors
• Linear perturbations of Hyperkahler metrics
• Elliptic constructions of hyperkaehler metrics I: The Atiyah-Hitchin manifold

Cited by in corpus (3)

• A 5d/2d/4d correspondence
• $\mathcal{N}=2$ super Yang-Mills theory in Projective Superspace
• Connecting Localization and Wall-Crossing via D-Branes