A replica path-integral calculation yields analytic large-N formulas for covariance statistics and participation dimension in nonlinear recurrent neural networks with quenched Gaussian disorder, confirmed by simulation.
Quantum Field Theory in the Large N Limit: a review
8 Pith papers cite this work, alongside 511 external citations. Polarity classification is still indexing.
8
Pith papers citing it
511
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abstract
We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies on constructing effective field theories for composite fields after integration over the original degrees of freedom. We first solve a general scalar $U(\phib^2)$ field theory for $N$ large and discuss various non-perturbative physical issues such as critical behaviour. We show how large $N$ results can also be obtained from variational calculations.We illustrate these ideas by showing that the large $N$ expansion allows to relate the $(\phib^2)^2$ theory and the non-linear $\sigma$-model, models which are renormalizable in different dimensions. Similarly, a relation between $CP(N-1)$ and abelian Higgs models is exhibited. Large $N$ techniques also allow solving self-interacting fermion models. A relation between the Gross--Neveu, a theory with a four-fermi self-interaction, and a Yukawa-type theory renormalizable in four dimensions then follows. We discuss dissipative dynamics, which is relevant to the approach to equilibrium, and which in some formulation exhibits quantum mechanics supersymmetry. This also serves as an introduction to the study of the 3D supersymmetric quantum field theory. Large $N$ methods are useful in problems that involve a crossover between different dimensions. We thus briefly discuss finite size effects, finite temperature scalar and supersymmetric field theories. We also use large $N$ methods to investigate the weakly interacting Bose gas. The solution of the general scalar $U(\phib^2)$ field theory is then applied to other issues like tricritical behaviour and double scaling limit.
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OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.
Leading coefficients of the thermal effective action for the large-N critical O(N) vector model in 3D with twist are computed via twisted partition function on S2 and path-integral methods, yielding consistent results.
Four-loop anomalous dimensions of φ^Q in scalar-QED are obtained via OPE, with beta functions and mass/field anomalous dimensions, validating OPE beyond pure scalar theories.
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.
Develops a Functorial QFT approach and applies it to analyze the O(N) model in AdS, focusing on crossed-channel diagram contributions to conformal block decomposition in the non-singlet sector.
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.
Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.
citing papers explorer
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Statistics of correlations in nonlinear recurrent neural networks
A replica path-integral calculation yields analytic large-N formulas for covariance statistics and participation dimension in nonlinear recurrent neural networks with quenched Gaussian disorder, confirmed by simulation.
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The OPE Approach to Renormalization: Operator Mixing
OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.
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Thermal effective action for the $O(N)$ vector model
Leading coefficients of the thermal effective action for the large-N critical O(N) vector model in 3D with twist are computed via twisted partition function on S2 and path-integral methods, yielding consistent results.
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Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion
Four-loop anomalous dimensions of φ^Q in scalar-QED are obtained via OPE, with beta functions and mass/field anomalous dimensions, validating OPE beyond pure scalar theories.
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Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.
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Strongly Coupled Quantum Field Theory in Anti-de Sitter Spacetime
Develops a Functorial QFT approach and applies it to analyze the O(N) model in AdS, focusing on crossed-channel diagram contributions to conformal block decomposition in the non-singlet sector.
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Coherent and dissipative dynamics at quantum phase transitions
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.
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Notes on Tensor Models and Tensor Field Theories
Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.