On Type IIA Penrose Limit and N=6 Chern-Simons Theories

TL;DR

This work studies the Type IIA Penrose limit of the ABJM/AdS${}_4$–$CP^3$ dual, obtaining a solvable plane-wave background and an exact string spectrum that is expressed in terms of ABJM operator dimensions. It identifies BMN-like operators in the ${\cal N}=6$ Chern-Simons theory and analyzes their leading anomalous dimensions, revealing a BMN scaling violation compared to the string theory prediction. The paper also connects the weak-coupling ABJM theory on ${S}^1\times S^2$ to a matrix-model description and demonstrates a Hagedorn/deconfinement transition, consistent with expectations from the dual string/M-theory side. Overall, it provides nontrivial checks of AdS${}_4$/CFT${}_3$ in the ABJM context, highlights new features of BMN-like limits in 3D, and motivates exact determinations of the coupling-dependent function linking gauge theory and string theory across regimes.

Abstract

Recently, Aharony, Bergman, Jafferis and Maldacena proposed that the N=6 Chern-Simons gauge theories are holographically dual to the M-theory backgrounds with multiple M2-branes on orbifolds C^4/Z_k. When k is large, they have the type IIA string description. In this paper we analyze the Penrose limit of this IIA background and express the string spectrum as the conformal dimensions of operators in the gauge theories. For BPS operators, we can confirm the agreements between the IIA string on plane waves and the gauge theories. We point out that there exist BMN-like operators in the gauge theories, though their holographic interpretation does not seem to be simple. Also we analyze the weak coupling limit of this theory and show that the Hagedorn/deconfinement transition occurs as expected.