Multitrace Deformations of Vector and Adjoint Theories and their Holographic Duals

TL;DR

This work develops a unified large-$N$ framework for studying multitrace deformations in 3d CFTs with holographic duals, connecting vector and adjoint theories to higher-spin bulk descriptions via a generalized AdS/CFT approach. It shows that classically marginal deformations, such as $V( ho) \sim \rho^3$, yield a modulus at a critical coupling $g_c$ and an IR flow toward an $O(N)$-singlet sector, while deformations beyond $g_c$ induce bulk and boundary instabilities. The authors formulate a universal effective-action formalism where multitrace deformations simply add $V(\sigma)$ to the CFT effective action, and demonstrate how this framework reproduces known results for vector and adjoint theories, including big crunch scenarios in AdS$_4$ when marginal triple-trace deformations are present. They further argue that UV completions involving irrelevant operators can stabilize the theory and prevent boundary-reaching singularities, highlighting a productive interplay between boundary UV physics and bulk dynamics. Overall, the paper clarifies when holographic instabilities reflect genuine bulk pathologies versus when they are resolved by UV physics, offering insights into the string-theoretic interpretation of such phenomena.

Abstract

We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS_4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. The resolution suggests that the instability may not survive in an appropriate UV completion of the CFT.