Systematic $1/N$ corrections for bosonic and fermionic vector models without auxiliary fields

Abstract

In this paper, colorless bilocal fields are employed to study the large $N$ limit of both fermionic and bosonic vector models. The Jacobian associated with the change of variables from the original fields to the bilocals is computed exactly, thereby providing an exact effective action. This effective action is shown to reproduce the familiar perturbative expansion for the two and four point functions. In particular, in the case of fermionic vector models, the effective action correctly accounts for the Fermi statistics. The theory is also studied non-perturbatively. The stationary points of the effective action are shown to provide the usual large $N$ gap equations. The homogeneous equation associated with the quadratic (in the bilocals) action is simply the two particle Bethe Salpeter equation. Finally, the leading correction in $\frac{1}{N}$ is shown to be in agreement with the exact $S$ matrix of the model.

24 pages, uses REVTEX macros. Replaced with final version to appear in Phys. Rev. D

References in corpus (4)

• Loop Space Hamiltonians And Field Theory Of Non-Critical Strings
• Compositeness Condition at the Next-to-Leading Order in the Nambu-Jona-Lasinio Model
• Effective actions of local composite operators --- case of ${\phi }^4$ theory, itinerant electron model, and QED
• The Master Field of QCD${}_2$ and the 'T Hooft Equation

Cited by in corpus (25)

• AdS_4/CFT_3 Construction from Collective Fields
• Large-N Collective Fields and Holography
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• A Derivation of AdS/CFT for Vector Models
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Collective Dipole Model of AdS/CFT and Higher Spin Gravity
• Effective Field Theories in the Large $N$ Limit
• 1/N and Loop Corrections in Higher Spin AdS_4/CFT_3 Duality
• Operators, Correlators and Free Fermions for SO(N) and Sp(N)
• Perturbative and Non-Perturbative Aspects in Vector Model/Higher Spin Duality
• Holography of Information in AdS/CFT
• Stable Fermion Bag Solitons in the Massive Gross-Neveu Model: Inverse Scattering Analysis
• Higher Spin Holography, RG, and the Light Cone
• Large-N Expansion as Semiclassical Approximation to the Third-Quantized Theory
• Large N bilocals at the infrared fixed point of the three dimensional O(N) invariant vector theory with a quartic interaction
• Equation of state for the 2+1 dimensional Gross-Neveu model at order 1/N
• Constructing the bulk at the critical point of three-dimensional large $N$ vector theories
• Quantum Error Correction and Holographic Information from Bilocal Holography
• Dynamical Symmetry and the Thermofield State at Large $N$
• Holography for Tensor models
• How universal is the Wigner distribution?
• Time Evolution in the External Field: the Unitarity Paradox
• Exactly Solvable Quantum Mechanical Models with Infinite Renormalization of the Wave Function
• Fermionic Vector Model Solitons in the Large N Limit