AdS/CFT for Four-Point Amplitudes involving Gravitino Exchange
Linda I. Uruchurtu
TL;DR
This work computes the tree-level four-point function of two dilatini and two dilaton-axion operators in type IIB supergravity on $AdS_{5}\times S^{5}$, illuminating the AdS/CFT correspondence at large $N$ and large $\lambda$ with a novel gravitino exchange. The amplitude comprises graviton, gravitino, and quartic contributions and is conveniently expressed through $\bar{D}$-functions (and inverted $W$-functions) to enable detailed OPE analyses. The authors demonstrate that long (string) states decouple at strong coupling, and they extract the anomalous dimensions of semi-short double-trace operators, notably finding $\Delta^{(1)}=-16/N^{2}$ for an exotic-channel operator of dimension $15/2$. The results are cross-checked against free-field OPEs and conformal symmetry constraints, reinforcing the consistency of AdS/CFT for fermionic correlators and providing a concrete framework for studying double-trace deformations and truncations in ${\mathcal N}=4$ SYM. This work thus advances the toolkit for fermionic AdS/CFT correlators and clarifies the role of the exotic channel in the OPE structure at strong coupling.
Abstract
In this paper we compute the tree-level four-point scattering amplitude of two dilatini and two axion-dilaton fields in type IIB supergravity in AdS5 x S5. A special feature of this process is that there is an "exotic" channel in which there are no singleparticle poles. Another novelty is that this process involves the exchange of a bulk gravitino. The amplitude is interpreted in terms of N = 4 supersymmetric Yang-Mills theory at large 't Hooft coupling. Properties of the Operator Product Expansion are used to analyze the various contributions from single- and double-trace operators in the weak and strongly coupled regimes, and to determine the anomalous dimensions of semi-short operators. The analysis is particularly clear in the exotic channel, given the absence of BPS states.