# A perturbative study of holographic mABJM theory

## TL;DR

This paper analytically investigates the holographic free energy of the mass-deformed ABJM model (mABJM) with ${\cal N}=2$ supersymmetry, confirming a key conjecture about R-charge independence using perturbative solutions of BPS equations.

## Contribution

It provides an analytic proof of a conjecture regarding R-charge independence in mABJM, utilizing a perturbative method to solve BPS equations with IR regularity.

## Key findings

- Confirmed R-charge independence of three chiral multiplets
- Provided analytic solutions to BPS equations in mABJM
- Validated previous numerical conjectures

## Abstract

Recently the calculation of holographic free energy for mass-deformed ABJM model (mABJM) with ${\cal N}=2$ supersymmetry and $SU(3)\times U(1)$ global symmetry was tackled by Bobev et al. in arXiv:1812.01026. We solve the associated BPS equations, requiring IR regularity, using a perturbative method proposed by one of us recently in axXiv:1902.00418. In particular, we provide an analytic proof of a crucial conjecture made in arXiv:1812.01026 based on numerical solutions: that the R-charge values of three chiral multiplets in mABJM should be independent of the IR values of a hypermultiplet scalar, which is holographically dual to the superpotential mass term.