On Projective Hoops: Loops in Hyperspace

Abstract

We (re)derive the propagators and Feynman rules for the massless scalar and vector multiplets in N=2 Projective Superspace ('Projective Hyperspace'). With these, we are able to calculate both the divergent and finite parts of 2, 3 & 4-point functions at 1-loop for N=2 Super-Yang-Mills theory (SYM) explicitly in Projective Hyperspace itself. We find that effectively only the coupling constant needs to be renormalized unlike in the N=1 case where an independent wavefunction renormalization is also required. This feature is similar to that of the background field gauge, even though we are using ordinary Fermi-Feynman gauge. The computation of 1-hoop beta-function is then straightforward and matches with the known result. We also show that it receives no 2-hoops contributions. All these calculations provide an alternative proof of the finiteness of N=4 SYM.

29 pages, 12 figures; Added a reference & modified introduction in v2

References in corpus (10)

• The Background Field Method for N = 2 Super Yang-Mills Theories in 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
• Effective Action of the N = 2 Maxwell Multiplet in Harmonic Superspace
• Nonholomorphic N=2 terms in N=4 SYM: 1-Loop Calculation in N=2 superspace
• Complete Low-Energy Effective action in N=4 SYM: a Direct N=2 Supergraph Calculation
• Deriving Projective Hyperspace from Harmonic
• Feynman Rules in N=2 projective superspace III: Yang-Mills multiplet
• AdS/CFT in superspace

Cited by in corpus (8)

• Integrability in N=2 superconformal gauge theories
• A new approach to curved projective superspace
• On conformal supergravity and harmonic superspace
• Improved Methods for Hypergraphs
• 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
• Five-dimensional non-Abelian supersymmetric Chern-Simons action in Projective Superspace