Five loop renormalization of phi³ theory with applications to the Lee-Yang edge singularity and percolation theory

We apply the method of graphical functions that was recently extended to six dimensions for scalar theories, to $\phi^3$ theory and compute the $\beta$ function, the wave function anomalous dimension as well as the mass anomalous dimension in the \overline{\mbox{MS}} scheme to five loops. From the results we derive the corresponding renormalization group functions for the Lee-Yang edge singularity problem and percolation theory. After determining the $\varepsilon$ expansions of the respective critical exponents to $\mathcal{O}(\varepsilon^5)$ we apply recent resummation technology to obtain improved exponent estimates in 3, 4 and 5 dimensions. These compare favourably with estimates from fixed dimension numerical techniques and refine the four loop results. To assist with this comparison we collated a substantial amount of data from numerical techniques which are included in tables for each exponent.Comment: 54 pages, 15 figures; v2: additional summary tables and references added - version to be published in PR

Looking through the QCD conformal window with perturbation theory

We study the conformal window of QCD using perturbation theory, starting from the perturbative upper edge and going down as much as we can towards the strongly coupled regime. We do so by exploiting the available five-loop computation of the $overline{{m MS}}$ $eta$-function and employing Borel resummation techniques both for the ordinary perturbative series and for the Banks-Zaks conformal expansion. Large-$n_f$ results are also used. We argue that the perturbative series for the $overline{{m MS}}$ $eta$-function is most likely asymptotic and non-Borel resummable, yet Borel resummation techniques allow to improve on ordinary perturbation theory. We find substantial evidence that QCD with $n_f=12$ flavours flows in the IR to a conformal field theory. Though the evidence is weaker, we find indications that also $n_f=11$ might sit within the conformal window. We also compute the value of the mass anomalous dimension $gamma$ at the fixed point and compare it with the available lattice results. The conformal window might extend for lower values of $n_f$, but our methods break down for n_f<11, where we expect that non-perturbative effects become important. A similar analysis is performed in the Veneziano limit

Renormalization group functions of φ4φ^4 theory in the MS-scheme to six loops

Subdivergences constitute a major obstacle to the evaluation of Feynman integrals and an expression in terms of finite quantities can be a considerable advantage for both analytic and numeric calculations. We report on our implementation of the suggestion by F. Brown and D. Kreimer, who proposed to use a modified BPHZ scheme where all counterterms are single-scale integrals. Paired with parametric integration via hyperlogarithms, this method is particularly well suited for the computation of renormalization group functions and easily automated. As an application of this approach we compute the 6-loop beta function and anomalous dimensions of the $\phi^4$ model

Renormalization group functions of φ4φ^4 theory in the MS-scheme to six loops

Subdivergences constitute a major obstacle to the evaluation of Feynman integrals and an expression in terms of finite quantities can be a considerable advantage for both analytic and numeric calculations. We report on our implementation of the suggestion by F. Brown and D. Kreimer, who proposed to use a modified BPHZ scheme where all counterterms are single-scale integrals. Paired with parametric integration via hyperlogarithms, this method is particularly well suited for the computation of renormalization group functions and easily automated. As an application of this approach we compute the 6-loop beta function and anomalous dimensions of the $\phi^4$ model

Minimally subtracted six loop renormalization of O(n)-symmetric φ 4 theory and critical exponents

We present the perturbative renormalization group functions of O ( n ) -symmetric ϕ 4 theory in 4 − 2 ϵ dimensions to the sixth loop order in the minimal subtraction scheme. In addition, we estimate diagrams without subdivergences up to 11 loops and compare these results with the asymptotic behavior of the beta function. Furthermore we perform a resummation to obtain estimates for critical exponents in three and two dimensions

lambda phi(4) theory - Part I. The symmetric phase beyond NNNNNNNNLO

Perturbation theory of a large class of scalar field theories in d &lt; 4 can be shown to be Borel resummable using arguments based on Lefschetz thimbles. As an example we study in detail the \u3bb\u3d54 theory in two dimensions in the Z2 symmetric phase. We extend the results for the perturbative expansion of several quantities up to N8LO and show how the behavior of the theory at strong coupling can be recovered successfully using known resummation techniques. In particular, we compute the vacuum energy and the mass gap for values of the coupling up to the critical point, where the theory becomes gapless and lies in the same universality class of the 2d Ising model. Several properties of the critical point are determined and agree with known exact expressions. The results are in very good agreement (and with comparable precision) with those obtained by other non-perturbative approaches, such as lattice simulations and Hamiltonian truncation methods