ABJM Membrane Instanton from Pole Cancellation Mechanism

TL;DR

This paper explores the structure of membrane instantons in ABJM theory, revealing a pole cancellation mechanism that generalizes to related superconformal Chern-Simons theories, ensuring finite polynomial coefficients.

Contribution

It demonstrates a pole cancellation mechanism in membrane instantons across a family of superconformal theories, extending understanding of non-perturbative effects in ABJM theory.

Findings

Poles in instanton coefficients cancel among different effects.

Finite quadratic polynomial coefficients are recovered at special parameter values.

The mechanism parallels worldsheet-instanton interactions in ABJM theory.

Abstract

The coefficients of the membrane instantons in the ABJM theory are known to be quadratic polynomials of the chemical potential. We show that, after deforming the ABJM theory into more general superconformal Chern-Simons theories labelled by (q,p) where the original ABJM theory corresponds to (q,p)=(1,1), we can decompose the membrane instanton into three types of non-perturbative effects with constant coefficients independent of the chemical potential. We find that, although these constants contain poles at certain values of q and p including the ABJM case, all of the poles cancel among themselves and the finite quadratic polynomial coefficients are reproduced at these values. This is similar to what happens between the membrane instantons and the worldsheet instantons in the ABJM theory.