Holographic Supergravity Dual to Three Dimensional N=2 Gauge Theory

TL;DR

The paper establishes a concrete AdS$_4$/CFT$_3$ duality by showing that a mass-deformed ${\cal N}=8$ Bagger-Lambert theory flows in three dimensions to an ${\cal N}=2$ fixed point with $SU(3)_I \times U(1)_R$ symmetry, which is holographically dual to a four-dimensional ${\cal N}=2$ holographic RG flow. It analyzes the four-dimensional ${\cal N}=8$ gauged supergravity with two critical points, derives the domain-wall flow, and maps bulk fields to IR boundary operators, including the Kahler potential evolution $K \sim \sum_i \Phi_i\bar{\Phi}_i$ in the UV to $K \sim (\sum_i \Phi_i\bar{\Phi}_i)^{3/2}$ in the IR. The work provides explicit operator identifications within the ${\rm OSp}(2|4)$ spectrum and shows how scaling dimensions and R-charges organize into long and short multiplets, yielding a detailed bulk–boundary correspondence. These results offer a solid framework for classifying mass deformations of M2-brane theories and pave the way for exploring nonsupersymmetric holographic flows in the AdS$_4\times S^7$ background.

Abstract

By examining the previously known holographic N=2 supersymmetric renormalization group flow solution in four dimensions, we describe the mass-deformed Bagger-Lambert theory, that has SU(3)_I x U(1)_R symmetry, by the addition of mass term for one of the four adjoint chiral superfields as its dual theory. A further detailed correspondence between fields of AdS_4 supergravity and composite operators of the infrared field theory is obtained.