Identification of Bulk coupling constant in Higher Spin/ABJ correspondence

Abstract

We study the conjectured duality between the $\mathcal{N}=6$ Vasiliev higher spin theory on $Ad{S}_4$ and 3d $\mathcal{N}=6$ superconformal Chern-Simons matter theory known as the ABJ theory. We discuss how the parameters in the ABJ theory should be related to the bulk coupling constant in the Vasiliev theory. For this purpose, we compute two-point function of stress tensor in the ABJ theory by using supersymmmetry localization. Our result justifies the proposal by arXiv:1504.00365 and determine the unknown coefficient in the previous work.

10 pages, v3: typos corrected

References in corpus (10)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Notes on SUSY Gauge Theories on Three-Sphere
• Higher Spins & Strings
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Exact results on ABJ theory and the refined topological string
• Higher spin AdS_3 holography with extended supersymmetry
• Quantum Phase Transitions in Mass-Deformed ABJM Matrix Model
• ABJM Theory with mass and FI deformations and Quantum Phase Transitions
• 3d mirror symmetry as a canonical transformation

Cited by in corpus (6)

• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• ABJ Quadrality
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• ABJ Theory in the Higher Spin Limit
• An exact limit of ABJM
• Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators