ABJM Membrane Instanton from Pole Cancellation Mechanism

Understand

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.