Results 1 - 10 of 1723
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[en] We formulate the renormalization group equation for Wilson loops in such a way as to make the analogy with spin systems more transparent. We thus obtain a quantity Z(g2) analogous to the anomalous dimension γ(g2) for spin systems. The value of Z(g2) at the non-trivial fixed point in 4 + epsilon dimensions gives the exponent eta defined by Peskin. (orig.)
[en] In a previous paper, one of us pointed out that the anomalous dimension matrices for all physical processes that have been calculated to date are complex symmetric, if stated in an orthonormal basis. In this paper we prove this fact and show that it is only true in a subset of all possible orthonormal bases, but that this subset is the natural one to use for physical calculations.
[en] We calculate the Adler D-function for SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the Adler function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant is first considered and generalized to the case of an arbitrary representation for the chiral matter superfields. The correctness of this all-order relation is explicitly verified at the three-loop level. The special renormalization scheme in which this all-order relation remains valid for the D-function and the anomalous dimension defined in terms of the renormalized coupling constant is constructed in the case of using the higher derivative regularization. The analytic expression for the Adler function for SQCD is found in this scheme to the order . The problem of scheme-dependence of the D-function and the NSVZ-like equation is briefly discussed.
[en] We present results for the gluon field anomalous dimension in perturbative QCD and derive the corresponding Beta function at five-loop order. All given results are valid for a general gauge group.
[en] The conventional absence of field renormalization in the local potential approximation (LPA) — implying a zero value of the critical exponent η — is shown to be incompatible with the logic of the derivative expansion of the exact renormalization group (RG) equation. We present a LPA with η≠0 that strictly does not make reference to any momentum dependence. Emphasis is made on the perfect breaking of the reparametrization invariance in that pure LPA (absence of any vestige of invariance) which is compatible with the observation of a progressive smooth restoration of that invariance on implementing the two first orders of the derivative expansion whereas the conventional requirement (η=0 in the LPA) precluded that observation
[en] We present the result of the three-loop anomalous dimension of non-singlet transversity operator in QCD for the Mellin moment N=16. The obtained result coincides with the prediction from (arXiv:1203.1022) and can serve as a confirmation of the correctness of the general expression for three-loop anomalous dimension of non-singlet transversity operator in QCD for the arbitrary Mellin moment.
[en] We propose a mechanism for calculating anomalous dimensions of higher-spin twist-two operators in N=4 SYM. We consider the ratio of the two-point functions of the operators and of their superconformal descendants or, alternatively, of the three-point functions of the operators and of the descendants with two protected half-BPS operators. These ratios are proportional to the anomalous dimension and can be evaluated at n-1 loop in order to determine the anomalous dimension at n loops. We illustrate the method by reproducing the well-known one-loop result by doing only tree-level calculations. We work out the complete form of the first-generation descendants of the twist-two operators and the scalar sector of the second-generation descendants
[en] We perform extensive three-loop tests of the hexagon bootstrap approach for structure constants in planar SYM theory. We focus on correlators involving two BPS operators and one non-BPS operator in the so-called sector. At three loops, such correlators receive wrapping corrections from mirror excitations flowing in either the adjacent or the opposing channel. Amusingly, we find that the first type of correction coincides exactly with the leading wrapping correction for the spectrum (divided by the one-loop anomalous dimension). We develop an efficient method for computing the second type of correction for operators with any spin. The results are in perfect agreement with the recently obtained three-loop perturbative data by Chicherin, Drummond, Heslop, Sokatchev  and by Eden . We also derive the integrand for general multi-particle wrapping corrections, which turns out to take a remarkably simple form. As an application we estimate the loop order at which various new physical effects are expected to kick-in.