ABJM membrane instanton from a pole cancellation mechanism

Abstract

The coefficients of the membrane instantons in the ABJM theory are known to be quadratic polynomials of the chemical potential. For better insight into this nonconstantness, we consider more general superconformal Chern--Simons theories labelled by two parameters $(q,p)$. In these theories, we show that the membrane instantons split into three types of nonperturbative effects, one more type compared with the previous observation. We also determine their explicit coefficients which are 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.