Searching for strongly coupled AdS matter with multi-trace deformations

TL;DR

The paper investigates whether exactly marginal multi-trace deformations can yield strongly coupled matter in AdS without spoiling the holographic CFT framework. Using conformal perturbation theory in a 2D $\mathcal{N}=(2,2)$ setup, it analyzes a triple-trace deformation built from a chiral primary and computes leading corrections to OPE data and four-point functions. It finds that certain single-trace OPE coefficients acquire order-$N^0$ corrections while the four-point function at order $\lambda^2$ decomposes into a finite sum of two conformal blocks, with no bulk-point singularity, signaling that the strong matter interactions arise from boundary data rather than local bulk interactions. This leads to the conclusion that holographic CFTs describing strongly coupled AdS matter are isolated in theory space or lie infinitely far on the conformal manifold from conventional holographic CFTs. The results illuminate the role of boundary terms in realizing strongly coupled bulk matter and set constraints on how (and whether) such theories can be connected perturbatively to standard holographic CFTs.

Abstract

Holographic CFTs admit a dual emergent description in terms of semiclassical general relativity minimally coupled to matter fields. While the gravitational interactions are required to be suppressed by the Planck scale, the matter sector is allowed to interact strongly at the AdS scale. From the perspective of the dual CFT, this requires breaking large-$N$ factorization in certain sectors of the theory. Exactly marginal multi-trace deformations are capable of achieving this while still preserving a consistent large-$N$ limit. We probe the effect of these deformations on the bulk theory by computing the relevant four-point functions in conformal perturbation theory. We find a simple answer in terms of a finite sum of conformal blocks, indicating that the correlators display no bulk-point singularities. This implies that the matter of the bulk theory is made strongly coupled by boundary terms rather than local bulk interactions. Our results suggest that holographic CFTs that describe strongly coupled AdS matter must be isolated points on the CFT landscape or sit infinitely far away on the conformal manifold from conventional holographic CFTs.

Figures (5)

• Figure 1: The exchange diagrams contributing to $\langle {\mathbf{O}}^\dagger(0){\mathbf{O}}^\dagger(x){\mathbf{O}}(1){\mathbf{O}}(\infty)\rangle_{c}\vert_{\lambda^2}$.
• Figure 2: The exchange diagrams contributing to $\langle \chi^\dagger(0){\mathbf{O}}^\dagger(x)\chi(1){\mathbf{O}}(\infty)\rangle_{c}\vert_{\lambda^2}$.
• Figure 3: The contours $\gamma_{1,2,3}$ in the complex $u_-$ plane.
• Figure 4: The deformation of the $\gamma_2$ contour in the complex $u_-$ plane.
• Figure 5: Deformations of the different contours that contribute to $\square(a,b,c;x,\bar{x})$.