Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions

TL;DR

The paper applies conformal partial wave analysis to dilaton-axion four-point functions in AdS/CFT to resolve the operator content of the SYM$_4$ holographic image at strong coupling. By analyzing OPEs of bilocal operators and employing CPW, it shows that at strong coupling all higher-spin currents with $l \ge 4$ decouple, leaving the energy-momentum tensor block and towers with $\lambda = 8 + 2t$, while confirming a $U(1)_Y$ symmetry through equal anomalous dimensions for related bilocals. It computes anomalous dimensions at $O(N^{-2})$ for composite towers and contrasts free-field and strong-coupling data, deriving explicit fusion constants and analytic continuations of AdS star integrals. The results illuminate how holographic four-point functions organize into protected and composite sectors at large $N$, with implications for testing AdS/CFT in strongly coupled gauge theories.

Abstract

Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields $\tildeΦ\tildeΦ$, $\tilde{C}\tilde{C}$ and $\tildeΦ\tilde{C}$, the conformal fields which are symmetric traceless tensors of rank $l$ and have dimensions $δ=2+l$ or $8+l+η(l)$ and $η(l)=\mathcal{O}(N^{-2})$ are identified. The unidentified fields have dimension $δ=λ+l+η(l)$ with $λ\geq 10$. The anomalous dimensions $η(l)$ are calculated at order $\mathcal{O}(N^{-2})$ for both $2^{-{1/2}}(-\tildeΦ\tildeΦ + \tilde{C}\tilde{C})$ and $2^{-{1/2}}(\tildeΦ\tilde{C} + \tilde{C}\tildeΦ)$ and are found to be the same, proving $U(1)_Y$ symmetry. The relevant coupling constants are given at order $\mathcal{O}(1)$.

Figures (4)

• Figure 1: Graphs $s, t, u$ for $A_0$ and $D_0$. For $B_0$ and $C_0$ only the graph $t$ contributes
• Figure 2: Graviton exchange graphs $s, t, u$ for $A_1$ and $D_1$ and $t$ for $B_1$ and $C_1$
• Figure 3: Dilaton exchange graphs for $D_1$
• Figure 4: The graphs for $B_1=C_1$