Four-point functions in N=4 supersymmetric Yang-Mills theory at two loops

Abstract

Four-point functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory are studied using N=2 harmonic superspace perturbation theory. The results are expressed in terms of differential operators acting on a scalar two loop integral. The leading singular behaviour is obtained in the limit that two of the points approach one another. We find logarithmic singularities which do not cancel out in the sum of all diagrams. It is confirmed that Green's functions of analytic operators are indeed analytic at this order in perturbation theory.

26 pages, standard latex, uses feynman.tex, typo corrections, Note added, to appear in Nucl. Phys. B

References in corpus (8)

• Gauge Theory Correlators from Non-Critical String Theory
• Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at Large N
• Field Theory Tests for Correlators in the AdS/CFT Correspondence
• On Four-point Functions in the CFT/AdS Correspondence
• Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory
• Extremal Correlators in the AdS/CFT Correspondence
• K-K excitations on AdS_5 x S^5 as N=4 ``primary'' superfields
• A note on four-point functions of conformal operators in N=4 Super-Yang Mills

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