Numbers and Functions in Quantum Field Theory

Abstract

We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, ${\gamma }_m$ of dimensionally regularized ${\varphi }^4$ theory in the minimal subtraction scheme up to seven loops.

26 pages, revised and updated. 7 loops phi^4 added

References in corpus (10)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• High-precision calculation of the 4-loop contribution to the electron g-2 in QED
• The massless higher-loop two-point function
• Revised value of the eighth-order QED contribution to the anomalous magnetic moment of the electron
• Gluing Ladders into Fishnets
• The Galois coaction on ${\varphi }^4$ periods
• Framings for graph hypersurfaces
• Motivic periods and the projective line minus three points
• The geometry of one-loop amplitudes

Cited by in corpus (81)

• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• 50 Years of Quantum Chromodynamics
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Analytic Structure of all Loop Banana Amplitudes
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• The critical O(N) CFT: Methods and conformal data
• Abelian Higgs model at four loops, fixed-point collision and deconfined criticality
• Critical behavior of Dirac fermions from perturbative renormalization
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Tropical Monte Carlo quadrature for Feynman integrals
• Multi-loop techniques for massless Feynman diagram calculations
• Closed strings as single-valued open strings: A genus-zero derivation
• Six-loop beta functions in general scalar theory
• Fractal dimension of critical curves in the $O(n)$-symmetric ${\varphi }^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models
• Critical behavior of the QED${}_3$-Gross-Neveu-Yukawa model at four loops
• Large $N_f$ quantum field theory
• Critical exponents from five-loop scalar theory renormalization near six-dimensions
• Long-range multi-scalar models at three loops
• Hepp's bound for Feynman graphs and matroids
• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
• An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order $1/N^2$
• Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
• Graphical functions in even dimensions
• Multiple zeta values in deformation quantization
• Three-dimensional $O(N)$-invariant ${\varphi }^4$ models at criticality for $N\ge 4$
• Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite $\mathbf{\epsilon }$
• General scalar renormalisation group equations at three-loop order
• Glue-and-Cut at Five Loops
• Diagram Reduction in Problem of Critical Dynamics of Ferromagnets: 4-Loop Approximation
• Renormalization and non-renormalization of scalar EFTs at higher orders
• The Hopf algebra structure of the $R^{\ast }$-operation
• Precise Critical Exponents of the O(N)-Symmetric Quantum field Model using Hypergeometric-Meijer Resummation
• Model A of critical dynamics: 5-loop $\epsilon$ expansion study
• Recursive computation of Feynman periods
• Weak-Coupling, Strong-Coupling and Large-Order Parametrization of the Hypergeometric-Meijer Approximants
• Perturbation expansions at large order: Results for scalar field theories revisited
• Interplay Between Approximation Theory and Renormalization Group
• Instantons or Renormalons? A Comment on phi4_4 Theory in the MS Scheme
• Navigating through the O(N) archipelago
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• Resummation in QFT with Meijer G-functions
• Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles
• Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group
• Six-loop anomalous dimension of the ${\varphi }^Q$ operator in the $O(N)$ symmetric model
• Self-similar extrapolation in quantum field theory
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• Iterating QCD scattering amplitudes in the high-energy limit
• Five loop minimal MOM scheme field and quark mass anomalous dimensions in QCD
• Derivative expansion for computing critical exponents of O(N) symmetric models at NNLO
• Conformal Triangles and Zig-Zag Diagrams
• Critical behavior of isotropic systems with strong dipole-dipole interaction: three-loop study
• Statistics of Feynman amplitudes in ${\varphi }^4$-theory
• An Introduction to Motivic Feynman Integrals
• Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; Resummation of perturbative renormalization functions from field theories
• Bubble diagram through the Symmetries of Feynman Integrals method
• Five loop renormalization of the Wess-Zumino model
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group
• Properties of the $\epsilon$-Expansion, Lagrange Inversion and Associahedra and the $O(1)$ Model
• The long road from Regge poles to the LHC
• Five-loop massless propagator integrals
• Further investigations into the graph theory of ${\varphi }^4$-periods and the $c_2$ invariant
• The full spectrum of AdS${}_5$/CFT${}_4$ II: Weak coupling expansion via the quantum spectral curve
• Exact result in N=4 SYM theory: Generalised double-logarithmic equation
• A special case of completion invariance for the $c_2$ invariant of a graph
• Continued functions and critical exponents: Tools for analytical continuation of divergent expressions in phase transition studies
• Continued functions and Borel-Leroy transformation: Resummation of six-loop ε-expansions from different universality classes
• Predicting Feynman periods in ${\varphi }^4$-theory
• Six dimensional ultraviolet completion of the $CP(N)$ $\sigma$ model at two loops
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere
• Search for an Ultraviolet Zero in the Seven-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory
• Generalized single-valued hyperlogarithms
• The wheel classes in the locally finite homology of ${\mathrm{GL}}_n(\mathbb{Z})$, canonical integrals and zeta values
• A tale of two Regge limits
• 100 Glorious Years of the Ising Model
• Critical Exponents of the O(N)-symmetric ${\varphi }^4$ Model from the \boldmath{\large{ ${\epsilon }^7$}} Hypergeometric-Meijer Resummation
• $c_2$ invariants of hourglass chains via quadratic denominator reduction
• Critical behavior of isotropic systems with strong dipole-dipole interaction from the functional renormalization group