{"arxiv_id":"2104.00593","incoming":{"papers":14,"sentences":29,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":2,"sentences":3,"quotes":[{"arxiv_id":"2209.10586","title":"Taming a resurgent ultra-violet renormalon","url":"/paper/2209.10586","section":"Trans-series and resurgent hyperasymptotics","sentence":"So now we recast the Broadhurst-Kreimer problem, in the manner of Borinksy, Dunne and Meynig [ref] , by setting $g(x)=γ(-3x)/x$, to obtain an ODE that is economically written as [equation] and has an unsummable formal perturbative solution [equation] The expansion coefficients behave as [equation] at large $n$, with a Stokes constant [equation] that can be determined, empirically, by considering a solution [equation] and retaining terms linear in $σ_1$ in the non-linear ODE.","intent_p":0.95,"contests_p":null},{"arxiv_id":"2112.10235","title":"Reduction of Order and Transseries Structure of Radiation Reaction","url":"/paper/2112.10235","section":"Reduction of order and LL∞","sentence":"Modifying Richardson extrapolation to account for logarithmic corrections (see Ref. [ref] and <ref>), the convergence is improved significantly, as shown in <ref>.","intent_p":0.84,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":3,"sentences":4,"quotes":[{"arxiv_id":"2402.09981","title":"Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points","url":"/paper/2402.09981","section":"Introduction","sentence":"In particular, QFT has a variety of applications, including two-dimensional QFTs [ref] , Chern-Simons theory [ref] , the three-dimensional $O(2N)$ model [ref] , four-dimensional nonsupersymmetric QFTs [ref] , six-dimensional $ϕ^3$ theory [ref] , and supersymmetric gauge theories in diverse dimensions [ref] .","intent_p":0.84,"contests_p":null},{"arxiv_id":"2210.01164","title":"Some results on Landau poles and Feynman diagram cut structure by Hopf algebra","url":"/paper/2210.01164","section":"Introduction","sentence":"Finally, let us note that the original two differential equations of Broadhurst and Kreimer have recently been very strikingly studied from a resurgence perspective in [ref] , and Bellon and collaborators investigated the anomalous dimension in the Wess-Zumino model [ref] in a similar context.","intent_p":0.99,"contests_p":null},{"arxiv_id":"2105.02220","title":"Resummation of quantum radiation reaction and induced polarization","url":"/paper/2105.02220","section":"Resummation of LAD","sentence":"To obtain the runaway solutions one would start with e.g. a trans-series-like ansatz; see e.g. the recent papers [ref] for trans-series solutions to differential equations.","intent_p":0.8,"contests_p":null}]}],"unlabelled_sentences":22},"outgoing":{"papers":67,"sentences":143,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":7,"sentences":9,"quotes":[{"arxiv_id":"math.CA/0608414","title":null,"url":"/paper/math.CA/0608414","section":"Introduction","sentence":"We employ the trans-series approach to the resurgence properties of non-linear differential equations, along the lines of [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"math.CA/0608408","title":null,"url":"/paper/math.CA/0608408","section":"Introduction","sentence":"We employ the trans-series approach to the resurgence properties of non-linear differential equations, along the lines of [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2009.01962","title":"Uniformization and Constructive Analytic Continuation of Taylor Series","url":"/paper/2009.01962","section":"Borel analysis of the perturbative expansion of the anomalous dimension","sentence":"The idea is to make a conformal map[Significantly higher precision can be obtained with a uniformization map [ref] , which is particularly useful if fewer perturbative terms are available.] from the cut Borel $t$ plane, based on the leading singularity at $t=+1$, to the unit disk in the $z$ plane: [equation] Note that this conformal map does not require knowledge of the nature of the leading Borel singularity, just its location.","intent_p":0.93,"contests_p":null},{"arxiv_id":"1711.04445","title":"Perturbative Expansions in QCD Improved by Conformal Mappings of the Borel Plane","url":"/paper/1711.04445","section":"Borel analysis of the perturbative expansion of the anomalous dimension","sentence":"We can resolve these higher Borel singularities using a conformal mapping method that has been widely used (albeit for different reasons) in the physics literature [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"hep-ph/0006089","title":"Improved Conformal Mapping of the Borel Plane","url":"/paper/hep-ph/0006089","section":"Borel analysis of the perturbative expansion of the anomalous dimension","sentence":"We can resolve these higher Borel singularities using a conformal mapping method that has been widely used (albeit for different reasons) in the physics literature [ref] .","intent_p":0.88,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":12,"sentences":21,"quotes":[{"arxiv_id":"hep-th/0012146","title":"Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality","url":"/paper/hep-th/0012146","section":"Perturbative Hopf-algebraic analysis of massless $ϕ^3$ theory in 6 dimensions","sentence":"Contrast this with the massless Yukawa theory in 4 dimensions where the corresponding nonlinear equation for the anomalous dimension is quadratic in $γ(a)$, and first order in derivatives with respect to $a$ [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2005.04265","title":"Non-Perturbative Completion of Hopf-Algebraic Dyson-Schwinger Equations","url":"/paper/2005.04265","section":"Perturbative Hopf-algebraic analysis of massless $ϕ^3$ theory in 6 dimensions","sentence":"Contrast this with the massless Yukawa theory in 4 dimensions where the corresponding nonlinear equation for the anomalous dimension is quadratic in $γ(a)$, and first order in derivatives with respect to $a$ [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"hep-th/9912093","title":"Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Pade-Borel resummation","url":"/paper/hep-th/9912093","section":"Perturbative Hopf-algebraic analysis of massless $ϕ^3$ theory in 6 dimensions","sentence":"Contrast this with the massless Yukawa theory in 4 dimensions where the corresponding nonlinear equation for the anomalous dimension is quadratic in $γ(a)$, and first order in derivatives with respect to $a$ [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"hep-th/9611150","title":"Dimensional Renormalization in phi^3 theory: ladders and rainbows","url":"/paper/hep-th/9611150","section":"Asymptotics of the perturbative solution of the Hopf-algebraic Dyson–Schwinger equation","sentence":"The rainbow approximation [ref] yields a simple closed-form algebraic expression for the anomalous dimension, which has a convergent expansion (for ease of comparison, we use the same normalization convention as in ([ref])): [equation] On the other hand, the chain approximation [ref] yields a divergent perturbative expansion of the anomalous dimension (once again with the same normalization convention as in ([ref])): [equation] Note that the first two terms of the rainbow, chain and Hopf approximations all agree, since they involve the same diagrams, but that the $a^3$ coefficient differs.","intent_p":0.94,"contests_p":null},{"arxiv_id":"1002.3634","title":"Asymptotics of the instantons of Painleve I","url":"/paper/1002.3634","section":"Logarithmic behavior in large-order growth","sentence":"The appearance of $log(x)$ terms in the trans-series starting at the second exponential order of the graded trans-series ([ref]) is reflected in the appearance of $log(n)$ corrections appearing in the subleading large-order growth of the coefficients of the fluctuation series beyond the original perturbative series $G_(0)(x)≡G_pert(x)$.[Analogous logarithmic large-order growth is seen in the Painlevé I equation [ref] .] To illustrate this phenomenon, consider the coefficients $a_n^(1,0,0)$ of the fluctuation series $ℱ_(1,0,0)(x)$, which appears in the first exponential term $G_(1)(x)$ in ([ref]).","intent_p":0.83,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":18,"sentences":18,"quotes":[{"arxiv_id":"hep-th/0012146","title":"Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality","url":"/paper/hep-th/0012146","section":"Introduction","sentence":"The perturbative Hopf alge­bra structure of Dyson–Schwinger equations of this model was formulated in the pioneering papers [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"hep-th/9912093","title":"Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Pade-Borel resummation","url":"/paper/hep-th/9912093","section":"Introduction","sentence":"The perturbative Hopf alge­bra structure of Dyson–Schwinger equations of this model was formulated in the pioneering papers [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"hep-th/9909126","title":"Renormalization in quantum field theory and the Riemann-Hilbert problem","url":"/paper/hep-th/9909126","section":"Introduction","sentence":"The seminal work of Kreimer and Connes showed that there is an underlying Hopf-algebraic structure to the renormalization of quantum field theory (QFT) [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"q-alg/9707029","title":"On the Hopf algebra structure of perturbative quantum field theories","url":"/paper/q-alg/9707029","section":"Introduction","sentence":"The seminal work of Kreimer and Connes showed that there is an underlying Hopf-algebraic structure to the renormalization of quantum field theory (QFT) [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"hep-th/0003188","title":"Renormalization in quantum field theory and the Riemann-Hilbert problem II: the $\\beta$-function, diffeomorphisms and the renormalization group","url":"/paper/hep-th/0003188","section":"Introduction","sentence":"The seminal work of Kreimer and Connes showed that there is an underlying Hopf-algebraic structure to the renormalization of quantum field theory (QFT) [ref] .","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":95},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/2104.00593"}}