$20'$ Five-Point Function from $AdS_5\times S^5$ Supergravity

TL;DR

This work develops a symmetry-based, Lagrangian-free bootstrap for tree-level five-point holographic correlators in $AdS_5\times S^5$, focusing on the $\mathbf{20'}$ operator. By splitting the correlator into singular (exchange) and regular (contact) parts and enforcing AdS factorization together with the Beem chiral algebra and $SO(6)$ twists, the authors obtain a complete five-point function and its Mellin representation, without needing the quintic Lagrangian. The Euclidean OPE analysis then yields new strong-coupling CFT data, including unprotected three-point functions and novel coefficients, while confirming protected data against free theory expectations. The results illustrate a constructive path to higher-point holographic functions, reveal links to conformal-block structures and twists, and point toward extensions to other backgrounds and potential hidden symmetries at strong coupling.

Abstract

We develop new techniques to compute five-point correlation functions from IIB supergravity on $AdS_5\times S^5$. Our methods rely entirely on symmetry and general consistency conditions, and eschew detailed knowledge of the supergravity effective action. We demonstrate our methods by computing the five-point function of the $\mathbf{20'}$ operator, which is the superconformal primary of the stress tensor multiplet. We also develop systematic methods to compute the five-point conformal blocks in series expansions. Using the explicit expressions of the conformal blocks, we perform a Euclidean OPE analysis of the $\mathbf{20'}$ five-point function. We find expected agreement with non-renormalized quantities and also extract new CFT data at strong coupling.

Figures (11)

• Figure 1: Each line between points $i$ and $j$ corresponds to a factor of $t_{ij}$. We can then see that there are two types of structures, $A_{(ijklm)}$ and $A_{(ijk)(lm)}$, with one and two closed cycles respectively. Note that each cycle is invariant under cyclic permutations and reflection, so the number of independent structures is given by the number of ways to distribute the points into the cycles, modulo those symmetries.
• Figure 2: The four types of double-exchange Witten diagrams allowed by R-symmetry selection rules. The straight, curly and double curly lines correspondingly represent the scalar, graviphoton and graviton field.
• Figure 3: The three types of single-exchange Witten diagrams allowed by R-symmetry selection rules. Here we have suppressed the derivative information in the quartic vertices.
• Figure 4: A contact Witten diagram. The information of derivatives in the quintic vertex is also suppressed in the diagram.
• Figure 5: Factorization on an internal graviton line. Here " perms" denotes the other inequivalent diagrams obtained by permuting the external legs 3, 4 and 5. Upon factorizing the five-point function on the internal graviton line, we obtain a three-point function $\langle \mathcal{O}_\mathbf{20'}\mathcal{O}_\mathbf{20'}\mathcal{T}_{\mu\nu}\rangle$ and a four-point function $\langle\mathcal{T}_{\mu\nu}\mathcal{O}_\mathbf{20'}\mathcal{O}_\mathbf{20'}\mathcal{O}_\mathbf{20'}\rangle$.