Instanton effects in ABJM theory with general R-charge assignments

TL;DR

This paper investigates how instanton effects in ABJM theory are affected by general R-charge deformations, revealing that certain structural features persist despite symmetry breaking, with implications for dual gravity theories.

Contribution

It extends the analysis of ABJM theory to include general R-charge assignments, uncovering the persistence of Airy function structures and identifying new non-perturbative effects.

Findings

Partition function retains Airy function form despite deformations

Five types of membrane instantons identified with deformation-dependent exponents

Singularities in instanton effects suggest observable gravity-side phenomena

Abstract

We study the large N expansion of the partition function of the quiver superconformal Chern-Simons theories deformed by two continuous parameters which correspond to the general R-charge assignment to the matter fields. Though the deformation breaks the conformal symmetry, we find that the partition function shares various structures with the superconformal cases, such as the Airy function expression of the perturbative expansion in 1/N with the overall constant A(k) related to the constant map in the ABJM case through a simple rescaling of k. We also identify five kinds of the non-perturbative effects in 1/N which correspond to the membrane instantons. The instanton exponents and the singular structure of the coefficients depend on the continuous deformation parameters, in contrast to the superconformal case where all the parameters are integers associated with the orbifold action on the moduli space. This implies that the singularity of the instanton effects would be observable also in the gravity side.