Non-renormalization of two and three Point Correlators of N=4 SYM in N=1 Superspace

Abstract

Certain two and three point functions of gauge invariant primary operators of $\mathcal{N}=4$ SYM are computed in $\mathcal{N}=1$ superspace keeping all the $þ$-components. This allows one to read off many component descendent correlators. Our results show the only possible $g_{YM}^2$ corrections to the free field correlators are contact terms. Therefore they vanish for operators at separate points, verifying the known non-renormalization theorems. This also implies the results are consistent with $\mathcal{N}=4$ supersymmetry even though the Lagrangian we use has only $\mathcal{N}=1$ manifest supersymmetry. We repeat some of the calculations using supersymmetric Landau gauge and obtain, as expected, the same results as those of supersymmetric Feynman gauge.

10 pages, 20 eps figures, references added

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• Three-Point Functions of Quarter BPS Operators in N=4 SYM
• Absorption of dilaton partial waves by D3-branes
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• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
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• Absorption by Double-Centered D3-Branes and the Coulomb Branch of N=4 SYM Theory
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• AdS/SCFT in Superspace
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• A Regularization Scheme for the AdS/CFT Correspondence
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• Structure of the Electric Flux in N=4 Supersymmetric Yang-Mills Theory
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