Qcd-like properties of anomalous dimensions in the $$ \mathcal{N} $$=4 supersymmetric Yang-Mills theory

Abstract

We show how closed formulas for the anomalous dimensions of two classes of operators in the N =4 supersymmetric Yang-Mills theory can be derived either based on numerical investigation or based on QCD-inspired assumptions. We consider the case of twist-3 "gauge" operators for which we completely prove the reciprocity.

One-loop spectroscopy of semiclassically quantized strings: bosonic sector

“…For completeness, we mention that the analysis for the LL folded string in the SL(2) sector (where strings rotate in AdS 3 ⊂ AdS 5 with center of mass moving along a big circle of S 5 ) is totally analogous. Using the following analytical continuation [24,32] 18) one can easily see that the system of coupled fluctuations is effectively described by the fourth order differential operator in (2.20) where now k 2 is negative. Its solutions are then trivially generalised to the case k 2 < 0 as basically in each formula one should substitute k → √ −k 2 and omit all imaginary constants i in the exponentials.…”

“…5 Another way in which sigma-model perturbation theory has been importantly used in the study of the integrable structure underlying the AdS/CFT system is the calculation of the worldsheet S-matrix, where results exists at tree-level [10], one-loop [11][12][13] and two-loop order [12] (for further references see [14]). 6 See for example, in the large spin limit, the detection of turning-point contributions for the energy of a single-spin string rotating in AdS5 [17] which are missed by naive perturbation theory, or the possibility to check at high orders the peculiar reciprocity-respecting structure of subleading corrections [18]. 7 In the single-spin case, fermions are naturally decoupled at quadratic level.…”