Electron Mass Anomalous Dimension at O(1/N^2_f) in Quantum Electrodynamics

The critical exponent corresponding to the renormalization of the composite operator $\bar{\psi}\psi$ is computed in quantum electrodynamics at O(1/\Nf^2) in arbitrary dimensions and covariant gauge at the non-trivial zero of the $\beta$-function in the large \Nf expansion and the exponent corresponding to the anomalous dimension of the electron mass which is a gauge independent object is deduced. Expanding in powers of $\epsilon$ $=$ $2$ $-$ $d/2$ we check it is consistent with the known three loop perturbative structure and determine the subsequent coefficients in the coupling constantComment: 12 pages (latex), 1 figure (available from author on request), LTH-31

Anomalous dimension of non-singlet quark currents at O(1/Nf^2) in QCD

We compute the O(1/Nf^2) corrections to the flavour non-singlet quark bilinear currents in QCD in arbitrary spacetime dimensions. Hence, the anomalous dimension of the QED current $\bar{\psi} \sigma^{\mu\nu} \psi$ is deduced at four loops in the MSbar scheme up to one unknown parameter.Comment: 8 latex page

The Nambu-Jona-Lasinio Model at O(1/N^2)

We write down the anomalous dimensions of the fields of the Nambu--Jona-Lasinio model or chiral Gross Neveu model with a continuous global chiral symmetry for the two cases $U(1)$ $\times$ $U(1)$ and $SU(M)$ $\times$ $SU(M)$ at $O(1/N^2)$ in a $1/N$ expansion.Comment: 9 latex pages, 4 figures (available on request from the author), LTH-308, (2 eqns corrected

Anomalous dimension of gluonic operator in polarized deep inelastic scattering at O(1/N_f)

We compute the O(1/N_f) correction to the predominantly gluonic flavour singlet twist-2 anomalous dimension used in polarized deep inelastic scattering. It is consistent with known two loop perturbation theory and we determine the three loop contribution at O(1/N_f). The treatment of the epsilon-tensor in the large N_f d-dimensional critical point formalism is also discussed.Comment: 8 Latex pages, 1 postscript figur

Quark, Gluon and Ghost Anomalous Dimensions at O(1/N_f) in Quantum Chromodynamics

By considering the scaling behaviour of various Feynman graphs at leading order in large \Nf at the non-trivial fixed point of the $d$-dimensional $\beta$-function of QCD we deduce the critical exponents corresponding to the quark, gluon and ghost anomalous dimensions as well as the anomalous dimensions of the quark-quark-gluon and ghost-ghost-gluon vertices in the Landau gauge. As the exponents encode all orders information on the perturbation series of the corresponding renormalization group functions we find agreement with the known three loop structure and, moreover, we provide new information at all subsequent orders.Comment: 13 pages latex plus 3 figures (available from author on request), LTH-31

Four loop MSbar mass anomalous dimension in the Gross-Neveu model

We compute the four loop term of the mass anomalous dimension in the two dimensional Gross-Neveu model in the MSbar scheme. The absence of multiplicative renormalizability which results when using dimensional regularization means that the effect of the evanescent operator, which first appears at three loops in the 4-point Green's function, has to be properly treated in the construction of the renormalization group function. We repeat the calculation of the three loop MSbar beta-function and construct the beta-function of the evanescent operator coupling which corrects earlier computations.Comment: 20 latex pages, 7 figure

QCD and QED renormalization group functions - a large N_f approach

The large N_f self-consistency programme is reviewed. As an application the QCD beta-function is computed at O(1/N_f) and the anomalous dimensions of polarized twist-2 singlet operators are determined at the same order.Comment: Talk given at DESY workshop QCD and QED in higher order; 8 pages latex plus 1 figur

Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering

We use the large N_f self consistency formalism to compute the $O(1/N_f)$ critical exponent corresponding to the renormalization of the flavour non-singlet twist two Wilson operators which arise in the operator product expansion of currents in deep inelastic processes. Expanding the $d$-dimensional expression in powers of $\epsilon$ $=$ $(4-d)/2$ the coefficients of $\epsilon$ agree with the known two loop structure of the corresponding renormalization group function and we deduce analytic expressions for all moments, $n$, at three and higher orders in perturbation theory in the \overline{\mbox{MS}} scheme at $O(1/N_f)$.Comment: 13 Latex pages, 1 figure (available from author on request), LTH-32

Computation of quark mass anomalous dimension at O(1/N_f^2) in quantum chromodynamics

We present the formalism to calculate d-dimensional critical exponents in QCD in the large N_f expansion where N_f is the number of quark flavours. It relies in part on demonstrating that at the d-dimensional fixed point of QCD the critical theory is equivalent to a non-abelian version of the Thirring model. We describe the techniques used to compute critical two and three loop Feynman diagrams and as an application determine the quark wave function, eta, and mass renormalization critical exponents at O(1/N_f^2) in d-dimensions. Their values when expressed in relation to four dimensional perturbation theory are in exact agreement with the known four loop MSbar results. Moreover, new coefficients in these renormalization group functions are determined to six loops and O(1/N_f^2). The computation of the exponents in the Schwinger Dyson approach is also provided and an expression for eta in arbitrary covariant gauge is given.Comment: 41 latex pages, 17 postscript figure

Renormalization properties of the mass operator A^2 in three dimensional Yang-Mills theories in the Landau gauge

Massive renormalizable Yang-Mills theories in three dimensions are analysed within the algebraic renormalization in the Landau gauge. In analogy with the four dimensional case, the renormalization of the mass operator A^2 turns out to be expressed in terms of the fields and coupling constant renormalization factors. We verify the relation we obtain for the operator anomalous dimension by explicit calculations in the large N_f. The generalization to other gauges such as the nonlinear Curci-Ferrari gauge is briefly outlined.Comment: 15 pages, 3 figure