Non-trivial fixed point of a ${\psi }_d^4$ fermionic theory, II. Anomalous exponent and scaling operators

Abstract

We consider the Renormalization Group (RG) fixed-point theory associated with a fermionic ${\psi }_d^4$ model in $d=1,2,3$ with fractional kinetic term, whose scaling dimension is fixed so that the quartic interaction is weakly relevant in the RG sense. The model is defined in terms of a Grassmann functional integral with interaction $V^{\ast }$, solving a fixed-point RG equation in the presence of external fields, and a fixed ultraviolet cutoff. We define and construct the field and density scale-invariant response functions, and prove that the critical exponent of the former is the naive one, while that of the latter is anomalous and analytic. We construct the corresponding (almost-)scaling operators, whose two point correlations are scale-invariant up to a remainder term, which decays like a stretched exponential at distances larger than the inverse of the ultraviolet cutoff. Our proof is based on constructive RG methods and, specifically, on a convergent tree expansion for the generating function of correlations, which generalizes the approach developed by three of the authors in a previous publication [A. Giuliani, V. Mastropietro, S. Rychkov, JHEP 01 (2021) 026].

arXiv comment60 pages, 11 figures. Final version accepted for publication on Comm. Math. Phys

References in corpus (24)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Polymers and percolation in two dimensions and twisted N=2 supersymmetry
• A line of CFTs: from generalized free fields to SYK
• Ward identities and Chiral anomaly in the Luttinger liquid
• Scaling limits and critical behaviour of the 4-dimensional n-component $|\phi {|}^4$ spin model
• A Complete Renormalization Group Trajectory Between Two Fixed Points
• Functional Integral Construction of the Thirring model: axioms verification and massless limit
• CRITICAL (Phi^{4}_{3,ε})
• Planar Ising magnetization field I. Uniqueness of the critical scaling limit
• Critical exponents for long-range O(n) models below the upper critical dimension
• Distributions in CFT II. Minkowski Space
• Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models
• Extended scaling relations for planar lattice models
• The scaling limit of the energy correlations in non integrable Ising models
• Field Theories for Loop-Erased Random Walks
• Non-integrable dimers: Universal fluctuations of tilted height profiles
• Critical correlation functions for the 4-dimensional weakly self-avoiding walk and n-component $|\phi {|}^4$ model
• Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric ${\varphi }^4$ theory with $n\to -2$ and loop-erased random walks
• Energy correlations of non-integrable Ising models: The scaling limit in the cylinder
• 3D Ising Model: a view from the Conformal Bootstrap Island
• Symplectic critical models in $6+\epsilon$ dimensions
• Finite-order correlation length for 4-dimensional weakly self-avoiding walk and $|\phi {|}^4$ spins
• Non-integrable Ising models in cylindrical geometry: Grassmann representation and infinite volume limit
• Constructing a weakly-interacting fixed point of the Fermionic Polchinski equation