M5 spikes and operators in the HVZ membrane theory

TL;DR

This paper investigates the spectrum of chiral operators, BPS solutions, and moduli space structures in the dual ABJM theory, revealing new branches and brane configurations, and matching supergravity modes with field theory operators.

Contribution

It provides a detailed analysis of the moduli space, BPS solutions, and operator spectrum in the dual ABJM theory, uncovering new branches and brane configurations not previously described.

Findings

Agreement of chiral operator spectrum with the mesonic moduli space

Discovery of an extra branch at the orbifold fixed point

Identification of two types of M5 spike configurations

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 M=C^2\times C^2/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 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 C^n\times CY_{4-n}.