Abelian Projections of the Mass-deformed ABJM theory and Weakly Curved Dual Geometry

Abstract

We construct $\mathcal{N}=2,4$ supersymmetric abelian projections of the $\mathcal{N}=6$ mass-deformed ABJM theory. There are well-defined dual background geometries for the $\mathcal{N}=2$ abelian theory, while those geometries are unclear for the $\mathcal{N}=4$ abelian theory. The $\mathcal{N}=2$ theory is built on the supersymmetric vacua of the mass-deformed ABJM theory, which are proven to have one-to-one correspondence with the ${\mathbb{Z}}_k$ quotient of Lin-Lunin-Maldacena geometries. We select one special vacuum of the mass-deformed ABJM theory and show that the corresponding geometry is weakly curved at every point of the entire space transverse to the M2-branes in the large $N$ limit.

arXiv comment31 pages, 5 figures, more analysis for gravitational invariants was added, published version

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• Renormalized Entanglement Entropy Flow in Mass-deformed ABJM Theory
• Holographic Entanglement Entropy of Mass-deformed ABJM Theory
• Holographic Entanglement Entropy of Anisotropic Minimal Surfaces in LLM Geometries
• Non-topological Vortex Configurations in the ABJM Model
• Holography of Massive M2-brane Theory with Discrete Torsion
• Holography of Massive M2-brane Theory: Non-linear Extension