Anomalous Dimension Of Twist-2 Operators Research Articles

Exact result in mathcal{N} = 4 SYM theory: generalised double-logarithmic equation

We present the new results for the generalised double-logarithmic equation, obtained from the analytical continuation of the seven-loop anomalous dimension of twist-2 operators in the planar mathcal{N} = 4 SYM theory. The double-logarithmic equation is related to the special asymptotic of the scattering amplitudes, when the large logarithms of the energy of scattering particles are appeared and should be summed in all order of perturbative theory. These large logarithms correspond to the poles of the analytically continued anomalous dimension. The generalised double-logarithmic equation includes the subleading logarithms. We have found, that the expansion of the generalised double-logarithmic equation can be ressumed in the form of rational functions with simple denominator. The solution of the generalised double-logarithmic equation provides a lot of information about the poles of the analytically continued anomalous dimension in all orders of perturbative theory. We have found also the generalised double-logarithmic equation for the analytically continued anomalous dimension near the value, which is related with BFKL-equation.

Twist-2 at seven loops in planar N $$ \mathcal{N} $$ = 4 SYM theory: full result and analytic properties

The anomalous dimension of twist-2 operators of arbitrary spin in planar N=4 SYM theory is found at seven loops by using the quantum spectral curve to compute values at fixed spin, and reconstructing the general result using the LLL-algorithm together with modular arithmetic. The result of the analytic continuation to negative spin is presented, and its relation with the recently computed correction to the BFKL and double-logarithmic equation is discussed.

Non-planar anomalous dimension of twist-2 operators: Higher moments at four loops

We compute the non-planar contribution to the anomalous dimension of the eighth moment of the twist-2 operators in N=4 supersymmetric Yang–Mills theory at four loops. This result was obtained from the calculations of some elements of the anomalous dimension matrix for twist-2 operators with the help of the relations between its elements and eigenvalues. The properties of the obtained result and possible relations with a planar results are discussed.

Twist-2 at five loops: wrapping corrections without wrapping computations

Using known all-loop results from the BFKL and generalized doublelogarithmic equations and large spin limit we have recomputed the five-loop planar anomalous dimension of twist-2 operators without consideration of any wrapping effects. One part of the anomalous dimension was calculated in an usual way with the help of Asymptotic Bethe Ansatz. The rest part, related with the wrapping effects, was reconstructed from a known constraints with the help of methods from the numbers theory.

Double-logs, Gribov-Lipatov reciprocity and wrapping

We study analytical properties of the five-loop anomalous dimension of twist-2 operators at negative even values of Lorentz spin. Following L. N. Lipatov and A. I. Onishchenko, we have found two possible generalizations of double-logarithmic equation, which allow to predict a lot of poles of anomalous dimension of twist-2 operators at all orders of perturbative theory from the known results. Second generalization is related with the reciprocity-respecting function, which is a single-logarithmic function in this case. We have found, that the knowledge of first orders of the reciprocity-respecting function gives all-loop predictions for the highest poles. Obtained predictions can be used for the reconstruction of a general form of the wrapping corrections for twist-2 operators.

The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: First moments in [formula omitted] SYM and non-singlet QCD

We present the result of a full direct component calculation for the first three even moments of the non-planar contribution into the four-loop anomalous dimension of twist-2 operators in maximally extended N = 4 supersymmetric Yang–Mills theory. Obtained result completes our previous calculations in arXiv:0902.4646 [9] and gives the usual result for the higher moments on the contrary to degenerate one in the case of Konishi. We propose a general form of ζ 5 and ζ 3 parts of the complete non-planar four-loop anomalous dimension of twist-2 operators. As by product, we have obtained the first even moment of the non-planar contribution to the non-singlet four-loop anomalous dimension of Wilson twist-2 operators in QCD.

Four loop reciprocity of twist two operators in 𝒩 = 4 SYM

The four loop universal anomalous dimension of twist-2 operators in N=4 SYM has been recently conjectured. In this paper, we prove that it obeys a generalized Gribov-Lipatov reciprocity, previously known to hold at the three loop level.

Eden-Staudacher and Beisert-Eden-Staudacher equations in the $$\mathcal{N} = 4$$ supersymmetric gauge theory

We investigate the Eden-Staudacher and Beisert-Eden-Staudacher equations for the anomalous dimension of twist-2 operators at a large spin s in the \(\mathcal{N} = 4\) supersymmetric gauge theory. We reduce these equations to a set of linear algebraic equations and calculate their kernels analytically. We demonstrate that in the perturbation theory, the anomalous dimension is a sum of products of the Euler functions ζ(k) having the maximum transcendentality property. We also show that at a large coupling, the “singular” solution of the Beisert-Eden-Staudacher equation reproduces the anomalous dimension constants predicted from the string side of the AdS/CFT correspondence.