Related papers: Multiple zeta functions and double wrapping in pla…
The cusp anomalous dimension is a ubiquitous quantity in four-dimensional gauge theories, ranging from QCD to maximally supersymmetric N=4 Yang-Mills theory, and it is one of the best investigated observables in the AdS/CFT correspondence.…
Anomalous dimensions of high-twist Wilson operators have a nontrivial scaling behavior in the limit when their Lorentz spin grows exponentially with the twist. To describe the corresponding scaling function in planar N=4 SYM theory, we…
We analyse the renormalisation properties of composite operators of scalar fields in the N=2 Super Yang-Mills theory. We compute the matrix of anomalous dimensions in the planar limit at one-loop order in the 't Hooft coupling, and show…
We revisit the strong coupling limit of the cusp anomalous dimension in planar N=4 super Yang-Mills theory. It is known that the strong coupling expansion is asymptotic and non-Borel summable. As a consequence, the cusp anomalous dimension…
Both for quark flavor asymmetry and valence, we consider the anomalous dimension of the non-singlet twist-two quark operator of arbitrary Lorentz spin N at four loops in SU(nc) color gauge theory and present its term proportional to zeta(3)…
We study SU(N) plane-wave matrix theory up to fourth perturbative order in its large N planar limit. The effective Hamiltonian in the closed su(2) subsector of the model is explicitly computed through a specially tailored computer program…
We study absolute zeta functions from the view point of a canonical normalization. We introduce the absolute Hurwitz zeta function for the normalization. In particular, we show that the theory of multiple gamma and sine functions gives good…
In this note we shall study the Witten multiple zeta function associated to the Lie algebra so(5) defined by Matsumoto. Our main result shows that its special values at nonnegative integers are always expressible by alternating Euler sums.…
The perturbative all-loop derivation of the NSVZ $\beta$-function for ${\cal N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives is finalized by calculating the sum of singularities produced by quantum…
We study multiple zeta values (MZVs) from the viewpoint of zeta-functions associated with the root systems which we have studied in our previous papers. In fact, the $r$-ple zeta-functions of Euler-Zagier type can be regarded as the…
In this paper we derive two expressions for the Hurwitz zeta function involving the complete Bell polynomials in the restricted case where q is a positive integer greater than 1. The arguments of the complete Bell polynomials comprise the…
We investigate the one-loop spectral problem of $\gamma$-twisted, planar $\mathcal{N}$=4 Super Yang-Mills theory in the double-scaling limit of infinite, imaginary twist angle and vanishing Yang-Mills coupling constant. This non-unitary…
We study regularization scheme dependence of K\"ahler ($N=2$) supersymmetric sigma models. At the one-loop order the metric $\beta$ function is the same as in non-supersymmetric case and coincides with the Ricci tensor. First correction in…
Adapting a method recently proposed by C. Marboe and D. Volin for ${\cal N}$=4 super-Yang-Mills, we develop an algorithm for a systematic weak coupling expansion of the spectrum of anomalous dimensions in the $sl(2)$-like sector of planar…
We use the principle of maximal transcendentality and the universal nature of subleading infrared poles to extract the analytic value of the four-loop collinear anomalous dimension in planar ${\cal N}=4$ super-Yang-Mills theory from recent…
We study the anomalous dimensions of operators in the scalar sector of \beta-deformed ABJ(M) theories. We show that the anomalous dimension matrix at two-loop order gives an integrable Hamiltonian acting on an alternating SU(4) spin chain…
Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in…
The large N limit of the anomalous dimensions of operators in ${\cal N}=4$ super Yang-Mills theory described by restricted Schur polynomials, are studied. We focus on operators labeled by Young diagrams that have two columns (both long) so…
We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find…
Non-linear integral equations derived from Bethe Ansatz are used to evaluate finite size corrections to the highest (i.e. {\it anti-ferromagnetic}) and immediately lower anomalous dimensions of scalar operators in ${\cal N}=4$ SYM. In…