Deriving Projective Hyperspace from Harmonic

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.

19 pages

References in corpus (16)

• (N,p,q) Harmonic Superspace
• The Background Field Method for N = 2 Super Yang-Mills Theories in Harmonic Superspace
• Projective Superspace as a Double--Punctured Harmonic Superspace
• On the D = 4, N = 2 Non-Renormalization Theorem
• Feynman Rules in N=2 Projective Superspace I: Massless hypermultiplets
• Feynman rules in N=2 projective Superspace II: Massive hypermultiplets
• Nonholomorphic N=2 terms in N=4 SYM: 1-Loop Calculation in N=2 superspace
• On Harmonic Superspaces and Superconformal Fields in Four Dimensions
• Effective action of N = 4 super Yang-Mills: N = 2 superspace approach
• Complete Low-Energy Effective action in N=4 SYM: a Direct N=2 Supergraph Calculation
• Super Multi-Instantons in Conformal Chiral Superspace
• Superfield representations of superconformal groups
• Feynman Rules in N=2 projective superspace III: Yang-Mills multiplet
• The Effective Action of N=8 Supergravity
• First-quantized N=4 Yang-Mills
• Superconformal spaces and implications for superstrings

Cited by in corpus (22)

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• Lectures on nonlinear sigma-models in projective superspace
• N=8 Supergravity on the Light Cone
• 2D N=(4,4) superspace supergravity and bi-projective superfields
• A new approach to curved projective superspace
• AdS/CFT in superspace
• N = 2 supersymmetric sigma-models and duality
• On conformal supergravity and harmonic superspace
• On 2D N=(4,4) superspace supergravity
• On Projective Hoops: Loops in Hyperspace
• Improved Methods for Hypergraphs
• A Q-Continuum of Off-Shell Supermultiplets
• Off-shell invariants of linearized $4D,\mathcal{N}=2$ supergravity in the harmonic approach
• N=2 Super-Yang-Mills Theory from a Chern-Simons Action
• $\mathcal{N}=2$ super Yang-Mills theory in Projective Superspace
• A Note on Massive Scalar Hypermultiplet in Projective Hyperspace
• Connecting Localization and Wall-Crossing via D-Branes
• Simplifying 4d $\mathcal{N}=3$ Harmonic Superspace
• Supersymmetric Sigma Model geometry
• The Dark Side of Double-Tensor Multiplets
• Five-dimensional non-Abelian supersymmetric Chern-Simons action in Projective Superspace
• $(0,4)$ Projective Superspaces I: Interacting Linear Sigma Models