M5 spikes and operators in the HVZ membrane theory

Abstract

In this note we study some aspects of the so-called dual ABJM theory introduced by Hanany, Vegh & Zaffaroni. We analyze the spectrum of chiral operators, and compare it with the spectrum of functions on the mesonic moduli space $\mathcal{M}{ = }{\mathbb{C}^2} \times {{{{\mathbb{C}^2}} \mathord{\left/{\vphantom {{{\mathbb{C}^2}} \mathbb{Z}}} \right.} \mathbb{Z}}_k}$, finding expected agreement for the coherent branch. A somewhat mysterious extra branch of dimension N ² opens up at the orbifold fixed point. We also study BPS solutions which represent M2/M5 intersections. The mesonic moduli space suggests that there should be two versions of this spike: one where the M5 lives in the orbifolded ${\mathbb{C}^2}$ and another where it lives in the unorbifolded one. While expectedly the first class turns out to be like the ABJM spike, the latter class looks like a collection of stacks of M5 branes with fuzzy S ³ profiles. This shows hints of the appearance of the global SO(4) at the non-abelian level which is otherwise not present in the bosonic potential. We also study the matching of SUGRA modes with operators in the coherent branch of the moduli space. As a byproduct, we present some formulae for the laplacian in conical CY ₄ of the form ${\mathbb{C}^n} \times C{Y_{4 - n}}$.