Deriving Projective Hyperspace from Harmonic

TL;DR

This paper introduces a method to derive projective N=2 superspace actions from harmonic superspace, including a novel nonabelian Yang-Mills action, using a Wick rotation technique that simplifies the internal space dimension.

Contribution

It presents a new derivation technique for projective superspace actions from harmonic superspace, notably deriving the nonabelian Yang-Mills action, and introduces a holographic perspective reducing internal space dimension.

Findings

Derived projective superspace actions from harmonic superspace.

Included a new derivation of nonabelian Yang-Mills action.

Demonstrated a holographic reduction of internal space dimension.

Abstract

We derive actions for projective N=2 superspace ("hyperspace") from those for harmonic hyperspace, including that for nonabelian Yang-Mills (a new result). The method uses Wick rotation of the sphere from complex conjugate coordinates to real, null ones, which can be treated as independent. The result can be considered "holographic" in that the dimension of the internal (R-symmetry) space is reduced from 2 to 1, by solving equations of motion or gauge conditions for dependence on the other coordinate. The auxiliary nature of the redundant dimension makes the hypergraph rules and evaluation almost identical.