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Operator product expansion of the lowest weight CPOs in \(\mathcal N=4\) \(\text{SYM}_ 4\) at strong coupling. (English) Zbl 1043.81709

Summary: We present a detailed analysis of the 4-point functions of the lowest weight chiral primary operators \(O^I\sim\text{tr}(\phi^{(i}\phi^{j)})\) in \(N=4 \text{SYM}_4\) at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence. In particular, all power-singular terms in the 4-point functions exactly coincide with the contributions coming from the conformal blocks of the CPOs, the R-symmetry current and the stress tensor. Operators dual to string modes decouple at strong coupling. We compute the anomalous dimensions and the leading \(1/N^2\) corrections to the normalization constants of the 2- and 3-point functions of scalar and vector double-trace operators with approximate dimensions 4 and 5, respectively. We also find that the conformal dimensions of certain towers of double-trace operators in the 105, 84 and 175 irreps are non-renormalized. We show that, despite the absence of a non-renormalization theorem for the double-trace operator in the 20 irrep, its anomalous dimension vanishes. As by-products of our investigation, we derive explicit expressions for the conformal block of the stress tensor, and for the conformal partial wave amplitudes of a conserved current and of a stress tensor in \(d\) dimensions.
An Erratum is given in ibid. 609, No. 3, 539 (2001).

MSC:

81T60 Supersymmetric field theories in quantum mechanics
83E30 String and superstring theories in gravitational theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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