A multitrace deformation of ABJM theory

TL;DR

This paper investigates a marginal triple trace deformation of ABJM theory, analyzing its effects on the boundary theory and bulk spacetime, including the emergence of big crunch singularities and the existence of a UV fixed point.

Contribution

It introduces and studies a new triple trace deformation of ABJM theory, exploring its renormalization group flow and implications for dual AdS spacetime singularities.

Findings

Beta function vanishes at large N, indicating a marginal deformation.

Existence of a perturbative UV fixed point in the zero 't Hooft coupling limit.

Extension of big crunch singularity analysis to orbifold models.

Abstract

Motivated by the study of big crunch singularities in asymptotically $AdS_4$ spacetimes, we consider a marginal triple trace deformation of ABJM theory. The deformation corresponds to adding a potential which is unbounded below. In a 't Hooft large N limit, the beta function for the triple trace deformation vanishes, which is consistent with the near-boundary behavior of the bulk fields. At the next order in the 1/N expansion, the triple trace couplings exhibit non-trivial running, which we analyze explicitly in the limit of zero 't Hooft coupling, in which the model reduces to an $O(N)\times O(N)$ vector model with large N. In this limit, we establish the existence of a perturbative UV fixed point, and we comment on possible non-perturbative effects. We also show that the bulk analysis leading to big crunch singularities extends to the $\Zbar_k$ orbifold models dual to ABJM theory.