Constructing the bulk at the critical point of three-dimensional large $N$ vector theories

Abstract

In the context of the $Ad{S}_4/CF{T}_3$ correspondence between higher spin fields and vector theories, we use the constructive bilocal fields based approach to this correspondence, to demonstrate, at the $IR$ critical point of the interacting vector theory and directly in the bulk, the removal of the $\Delta =1$ ($s=0$) state from the higher spins field spectrum, and to exhibit simple Klein-Gordon higher spin Hamiltonians. The bulk variables and higher spin fields are obtained in a simple manner from boundary bilocals, by the change of variables previously derived for the $UV$ critical point (in momentum space), together with a field redefinition.

arXiv commentDerivation of the Δ=2 Hamiltonian added to Section 3.3; 19 pages including references

References in corpus (13)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• AdS Dual of the Critical O(N) Vector Model
• Quantum Field Theory in the Large N Limit: a review
• Chern-Simons Theory with Vector Fermion Matter
• AdS_4/CFT_3 Construction from Collective Fields
• Holographic dual of free field theory
• Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory
• On Higher Spin Gauge Theory and the Critical O(N) Model
• ABJ Triality: from Higher Spin Fields to Strings
• Systematic $1/N$ corrections for bosonic and fermionic vector models without auxiliary fields
• Supersymmetric Higher Spin Theories
• Collective Dipole Model of AdS/CFT and Higher Spin Gravity

Cited by in corpus (2)

• Symmetry-resolved modular correlation functions in free fermionic theories
• Holography of Information in AdS/CFT