arXiv subjects
Publications and source records attributed to J. A. Gracey.
We use the large $N$ critical point formalism to examine the interplay of supersymmetry and chiral symmetry on the location or otherwise of multiple zetas in the renormalization group functions of several related field theories. In particular we determine that the anomalous dimension of the matter field of the Lagrangian corresponding to the bosonic sector of the $O(N)$ Wess-Zumino is free of multiple zetas to $O(1/N^3)$.
We assess the accuracy of our previous Asymptotic Padé predictions of the five-loop QCD $β$-function and quark mass anomalous dimension in the light of subsequent exact results. We find the low-order coefficients in an expansion in powers of $N_F$ (the number of flavours) were correct to within $1\%$. Furthermore an examination of recent results in $λϕ^4$ theory indicates that the Asymptotic Padé methods deliver predictions which increase in accuracy with loop order. Encouraged by this, we present six-loop Asymptotic Padé predictions for the QCD $β$-function and quark mass anomalous dimension, and also for the eight-loop $β$-function in $O(N)$ $λϕ^4$ theory.
We renormalize generalized 3-quark operators that relate to baryon states using the method devised by Kränkl and Manashov at four loops in the MSbar scheme. The anomalous dimensions of the four core operators used to compute nucleon matrix elements are determined and their associated critical exponents are studied in the conformal window using the Banks-Zaks expansion.
Using the recent six loop renormalization group functions for Lee-Yang and percolation theory constructed by Schnetz from a scalar cubic Lagrangian, we deduce the $ε$ expansion of the critical exponents for both cases. Estimates for the exponents in three, four and five dimensions are extracted using two-sided Padé approximants and shown to be compatible with values from other approaches.
We renormalize the Gross-Neveu-Yukawa model with an $O(N)$ symmetry to $\mathcal{O}(ε^5)$ in $d=4-ε$ dimensions and determine the anomalous dimensions of the fermion and scalar fields, $β$-functions as well as the scalar field's mass operator. These are used to construct several $N$ dependent critical exponents relevant for quantum transitions in semi-metals and in particular those connected with graphene in three dimensions when $N=2$. Improved exponent estimates for scalar fermion transitions on a honeycomb lattice, when $N=1$, as well as for $N=5$ are also given to compare with results from other techniques such as the conformal bootstrap.
We renormalize Quantum Chromodynamics (QCD) when gauge fixed in the nonlinear Curci-Ferrari gauge to four loops in the modified minimal subtraction (MSbar) scheme. We reproduce the four loop QCD MSbar beta-function from the Slavnov-Taylor identity for this gauge which relates the coupling constant renormalization to the gluon, Faddeev-Popov ghost and gauge parameter anomalous dimensions. This is carried out for a nonzero gauge parameter, without having to evaluate a vertex function. The anomalous dimension of the BRST invariant dimension two gluon and ghost mass term is deduced from a similar Slavnov-Taylor identity for this gauge. Consequently we construct the renormalization group functions in the minimal momentum subtraction scheme to four loops. As a corollary we deduce the five loop beta-function and quark mass anomalous dimensions in the same scheme. We also outline the pros and cons of employing the Curci-Ferrari gauge to access the six loop QCD beta-function in the MSbar scheme.
We evaluate the Green's function for the insertion of the second moment of the twist-$2$ flavour nonsinglet Wilson operator in a quark $2$-point function in all three different single scale external momentum configurations at four loops in the MSbar scheme and the chiral limit. One configuration is where the operator is inserted at zero momentum while the other two are where a non-zero momentum flows out through the operator itself with one external quark momentum nullified. In the latter two configurations mixing of the operator with a total derivative twist-$2$ operator is included for renormalization group consistency. In addition we compute the correlation functions of both gauge invariant operators to four loops in the same scheme.
We employ the Forcer algorithm to renormalize a variety of six dimensional field theories to four loops. In order to achieve this we construct the Forcer master integrals in six dimensions from their four dimensional counterparts by using the Tarasov method. The $ε$ expansion of the six dimensional masters are determined up to weight $9$ where $d$ $=$ $6$ $-$ $2ε$. By applying the Forcer routine the four loop MSbar renormalization of $ϕ^3$ theory is reproduced before gauge theories are considered. The renormalization of these theories is also determined in the MOMt scheme. For instance the absence of $ζ_4$ and $ζ_6$ is confirmed to five loops in the MOMt renormalization of $ϕ^3$ theory. We also evaluate the three loop $β$-function of the gauge coupling in six dimensional QCD.
We report on recent work on a class of renormalization schemes in QCD, termed the MOMt schemes. None of the renormalization group functions of the eight QCD MOMt schemes involve even zetas to five loops. A new scheme is introduced for scalar $ϕ^3$ theory in six dimensions where the full Laurent series in the regularizing parameter of the Green's function is absorbed into the renormalization constants. Designated as the MaxSbar scheme it is equivalent to the MOMt scheme in the critical dimension.
We examine a variety of renormalization schemes in QCD based on its $3$-point vertices where the $β$-functions, gluon, ghost, quark and quark mass anomalous dimensions in each scheme do not depend on $ζ_4$ or $ζ_6$ in an arbitrary linear covariant gauge at five loops. We comment on the $C$-scheme.
The Bjorken sum rule and R ratio are constructed to $O(a^4)$ in the Landau gauge in the three momentum subtraction schemes of Celmaster and Gonsalves where $a$ $=$ $g^2/(16π^2)$. We aim to examine the issue of convergence for observables in the various schemes as well as to test ideas on whether using the discrepancy in different scheme values is a viable and more quantum field theoretic alternative to current ways of estimating the theory error on a measureable.
We examine Crewther's relation at high loop order in perturbative QCD and demonstrate how the relation is accommodated in gauge-parameter dependent schemes where the running of the gauge parameter has to be explicitly considered. Motivated by ensuring that the conformal properties of the relation are preserved at all the critical points of QCD, including the Banks-Zaks and its infra-red stable twin, we demonstrate the necessity of an additional term in the relation for describing gauge running in the minimal momentum subtraction scheme (mMOM) and argue for its inclusion for all gauge-parameter dependent schemes.
We investigate the Crewther relation at high loop order in a variety of renormalization schemes and gauges. By examining the properties of the relation in schemes other than modified minimal subtraction (MSbar) at the fixed points of Quantum Chromodynamics we propose a generalization of the Crewther relation that extends the MSbar construction of Broadhurst and Kataev. A derivation based on the properties of the renormalization group equation is provided for the generalization which is tested in various scenarios.
We analyse the fixed points of QCD at high loop order in a variety of renormalization schemes and gauges across the conformal window. We observe that in the minimal momentum subtraction scheme solutions for the Banks-Zaks fixed point persist for values of Nf below that of the MSbar scheme in the canonical linear covariant gauge. By treating the parameter of the linear covariant gauge as a second coupling constant we confirm the existence of a second Banks-Zaks twin critical point, which is infrared stable, to five loops. Moreover a similar and parallel infrared stable fixed point is present in the Curci-Ferrari and maximal abelian gauges which persists in different schemes including kinematic ones. We verify that with the increased available loop order critical exponent estimates show an improvement in convergence and agreement in the various schemes.
We determine the anomalous dimensions of the gluon, Faddeev-Popov ghost and quark in the minimal MOM scheme to five loops for a general colour group when Quantum Chromodynamics is fixed in a linear covariant gauge. The quark mass anomalous dimension is also constructed in the same scheme.
We construct the five loop anomalous dimensions of the basic fields in Quantum Chromodynamics in a linear covariant gauge in the modified Regularization Invariant (RI') scheme. Using these core results we also compute the four loop Green's function where the quark mass operator and vector current are separately inserted in a quark 2-point function. These are necessary for measurements of the same quantities on the lattice. The Green's functions are provided in both the modified Minimal Subtraction (MSbar) and RI' schemes. All the results are available for a general Lie group.
We renormalize models with scalar chiral superfields with an odd superpotential to several orders in perturbation theory. These extensions of the cubic Wess-Zumino model are renormalizable in spacetime dimensions which are rational. When endowed with an $O(N)$ symmetry it is shown that they share the same property as their non-supersymmetric counterparts in that at a particular fixed point there is an emergent $OSp(1|n-1)$ symmetry, where $n$ is the power of the superpotential. This is shown at a loop order beyond that for which it was established in the parallel non-supersymmetric theory.
To assist the matching of lattice field theory results to the high energy continuum limit we evaluate the Green's function where the tensor quark bilinear operator is inserted at zero momentum in a quark $2$-point function for an arbitrary covariant gauge. This is carried out in both the MSbar and RI' schemes to four loops. The tensor current anomalous dimension is also calculated to four loops in both schemes for an arbitrary colour group.