Non-renormalization of next-to-extremal correlators in N=4 SYM and the AdS/CFT correspondence

Abstract

We show that next-to-extremal correlators of chiral primary operators in N=4 SYM theory do not receive quantum corrections to first order in perturbation theory. Furthermore we consider next-to-extremal correlators within AdS supergravity. Here the exchange diagrams contributing to these correlators yield results of the same free-field form as obtained within field theory. This suggests that quantum corrections vanish at strong coupling as well.

Figures (9)

• Figure 1: A dashed line connecting two solid lines indicates the effective four-scalar interaction resulting from gluon exchange and from the quartic vertex. Scalar propagators are denoted by solid lines and gluon propagators by wavy lines.
• Figure 2: Feynman diagrams contributing to the correlator $\langle \hbox{Tr} X^4(w) \hbox{Tr} X^2(x) \hbox{Tr} X^2(y)$$\hbox{Tr} X^2(z) \rangle$ at the free-field level.
• Figure 3: Feynman diagrams contributing to the correlator $\langle \hbox{Tr} X^4(w) \hbox{Tr} X^2(x) \hbox{Tr} X^2(y)$$\hbox{Tr} X^2(z) \rangle$ at order $g^2$. We do not show explicitly diagrams that are obtained from these by permutations of the operators. In diagrams $c$ and $d$, the dashed line can be connected to any of the two solid lines between $x$ and $w$.
• Figure 4: Feynman diagrams contributing to the correlator $\langle \hbox{Tr} X^{k_1}(w) \hbox{Tr} X^{k_2}(x) \hbox{Tr} X^{k_3}(y)$$\hbox{Tr} X^{k_4}(z) \rangle$ at the free-field level. Diagrams are drawn for $k_1=8$, $k_2=3$, $k_3=4$ and $k_4=3$. For arbitrary values of $k_i$, solid lines have to be added to or removed from the different "rainbows".
• Figure 5: Feynman diagrams contributing to the correlator $\langle \hbox{Tr} X^{k_1}(w) \hbox{Tr} X^{k_2}(x) \hbox{Tr} X^{k_3}(y)$$\hbox{Tr} X^{k_4}(z) \rangle$ at order $g^2$. As in Fig. 4, diagrams are drawn for $k_1=8$, $k_2=3$, $k_3=4$ and $k_4=3$. The dashed lines can be connected to any of the solid lines in each "rainbow". Here and in the following, permutations are not shown explicitly. Diagram $h$ is just one of the various diagrams that have two tadpoles connected by a dashed line.