Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group

Abstract

It is expected that conformal symmetry is an emergent property of many systems at their critical point. This imposes strong constraints on the critical behavior of a given system. Taking them into account in theoretical approaches can lead to a better understanding of the critical physics or improve approximation schemes. However, within the framework of the non-perturbative or functional renormalization group and, in particular, of one of its most used approximation schemes, the Derivative Expansion (DE), non-trivial constraints only apply from third order (usually denoted $\mathcal{O}({\partial }^4)$), at least in the usual formulation of the DE that includes correlation functions involving only the order parameter. In this work, we implement conformal constraints on a generalized DE including composite operators and show that new constraints already appear at second order of the DE (or $\mathcal{O}({\partial }^2)$). We show how these constraints can be used to fix nonphysical regulator parameters.

20 pages, 10 figures

References in corpus (50)

• Exact evolution equation for the effective potential
• Critical Phenomena and Renormalization-Group Theory
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Aspects of the Functional Renormalisation Group
• Critical Exponents of the N-vector model
• Solving the 3D Ising Model with the Conformal Bootstrap
• The nonperturbative functional renormalization group and its applications
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• An Introduction to the Nonperturbative Renormalization Group
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Derivative Expansion of the Exact Renormalization Group
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• Carving out OPE space and precise $O(2)$ model critical exponents
• Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
• A new method to solve the Non Perturbative Renormalization Group equations
• Numbers and Functions in Quantum Field Theory
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Monte Carlo study of an improved clock model in three dimensions
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Derivative expansion of the renormalization group in O(N) scalar field theory
• Non Perturbative Renormalization Group study of reaction-diffusion processes and directed percolation
• Supersymmetry and its spontaneous breaking in the random field Ising model
• Nonperturbative functional renormalization group for random field models: the way out of dimensional reduction
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Quantitative Phase Diagrams of Branching and Annihilating Random Walks
• Critical exponents can be different on the two sides of a transition: A generic mechanism
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach
• Scale invariance implies conformal invariance for the three-dimensional Ising model
• Restoring isotropy in a three-dimensional lattice model: The Ising universality class
• Bound states of the ${\varphi }^4$ model via the nonperturbative renormalization group
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• A glassy phase in quenched disordered graphene and crystalline membranes
• Numerical RG-time integration of the effective potential: Analysis and Benchmark
• Continued functions and perturbation series: Simple tools for convergence of diverging series in $O(n)$-symmetric ${\varphi }^4$ field theory at weak coupling limit
• The regulator dependence in the functional renormalization group: a quantitative explanation
• The $\lambda$-point anomaly in view of the seven-loop Hypergeometric resummation for the critical exponent $\nu$ of the $O(2)$ ${\varphi }^4$ model
• On Functional Representations of the Conformal Algebra
• Conformal invariance and vector operators in the $O(N)$ model
• A structural test for the conformal invariance of the critical 3d Ising model
• A Conformal Fixed-Point Equation for the Effective Average Action
• Construction of the Energy-Momentum Tensor for Wilson Actions
• Derivative expansion for computing critical exponents of O(N) symmetric models at NNLO

Cited by in corpus (3)

• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group
• Explicit construction of the energy-momentum tensor in the large N limit
• $SO(1,d+1)$ symmetry of the Exact RG equation