89 research outputs found
Four loop reciprocity of twist two operators in N=4 SYM
No full textThe complete universal anomalous dimension of twist-2 operators in N=4 SYM has been recently conjectured at four loops in terms of maximum transcendentality combinations of harmonic sums. It reproduces the known cusp anomaly, NLO BFKL poles, and the diagrammatic result for the Konishi operator. In this paper, we prove that it passes a further deep test related to a generalized Gribov-Lipatov reciprocity. This holds for both the asymptotic Bethe Ansatz contribution and the novel wrapping correction. This result suggests reciprocity to be a very stable and intrinsic property of twist-2 operators
Qcd-like properties of anomalous dimensions in the NN =4 supersymmetric Yang-Mills theory
No full textWe show how closed formulas for the anomalous dimensions of two classes of operators in the =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
Anomalous dimensions of finite size field strength operators in N=4 SYM
No full textIn the Script N = 4 super Yang-Mills theory, we consider the higher order anomalous dimensions γL(g) of purely gluonic operators Tr Script FL where Script F is a component of the self-dual field strength. We propose compact closed expressions depending parametrically on L that reproduce the prediction of Bethe Ansatz equations up to five loop order, including transcendental dressing corrections. The size dependence follows a simple pattern as the perturbative order is increased and suggests hidden relations for these special operators
Reciprocity of gauge operators in N=4SYM
No full textA recently discovered generalized Gribov-Lipatov reciprocity holds for the anomalous dimensions of various twist operators in Script N = 4 SYM. Here, we consider a class of scaling operators that reduce at one-loop to twist-3 maximal helicity gluonic operators. We extract from the asymptotic long-range Bethe Ansatz a closed expression for the spin dependent anomalous dimension at four loop order and provide a complete proof of reciprocity. We comment about the interplay with possible, yet unknown, wrapping corrections
Generalized Gribov-Lipatov Reciprocity and AdS/CFT
No full textPlanar
=4
SYM theory and QCD share the gluon sector, suggesting the investigation
of Gribov-Lipatov reciprocity in the supersymmetric theory. Since the
AdS/CFT correspondence links
=4
SYM and superstring dynamics on
Ad
S
5
×
S
5
, reciprocity is also expected to show up in the quantum corrected energies of certain
classical string configurations dual to gauge theory twist-operators. We review recent
results confirming this picture and revisiting the old idea of Gribov-Lipatov reciprocity
as a modern theoretical tool useful for the study of open problems in AdS/CFT
Twist-three at five loops, Bethe ansatz and wrapping
No full textWe present a formula for the five-loop anomalous dimension of N=4 SYM twist-three operators in the sl(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Luescher formalism, considering scattering processes of spin chain magnons with virtual particles that travel along the cylinder. The complete result respects the expected large spin scaling properties and passes non-trivial tests including reciprocity constraints. We analyze the pole structure and find agreement with a conjectured resummation formula. In analogy with the twist-two anomalous dimension at four-loops, wrapping effects are of order log^2 M/M^2 for large values of the spin
The scaling function at strong coupling from the quantum string Bethe equations
No full textWe study at strong coupling the scaling function describing the large spin anomalous dimension of twist two operators in Script N = 4 super Yang-Mills theory. In the spirit of AdS/CFT duality, it is possible to extract it from the string Bethe Ansatz equations in the fraktur sfraktur l(2) sector of the AdS5 × S5 superstring. To this aim, we present a detailed analysis of the Bethe equations by numerical and analytical methods. We recover several short string semiclassical results as a check. In the more difficult case of the long string limit providing the scaling function, we analyze the strong coupling version of the Eden-Staudacher equation, including the Arutyunov-Frolov-Staudacher phase. We prove that it admits a unique solution, at least in perturbation theory, leading to the correct prediction consistent with semiclassical string calculations
Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT1
No full textWe study local operator insertions on 1/2-BPS line defects in ABJM theory. Specifically, we consider a class of four-point correlators in the CFT1 with SU(1, 1|3) super- conformal symmetry defined on the 1/2-BPS Wilson line. The relevant insertions belong to the short supermultiplet containing the displacement operator and correspond to fluctuations of the dual fundamental string in AdS4× CP3 ending on the line at the boundary. We use superspace techniques to represent the displacement supermultiplet and we show that superconformal symmetry determines the four-point correlators of its components in terms of a single function of the one-dimensional cross-ratio. Such function is highly constrained by crossing and internal consistency, allowing us to use an analytical bootstrap approach to find the first subleading correction at strong coupling. Finally, we use AdS/CFT to compute the same four-point functions through tree-level AdS2 Witten diagrams, producing a result that is perfectly consistent with the bootstrap solution
Precision calculation of 1/4-BPS Wilson loops in AdS×S
No full textWe study the strong coupling behaviour of 1/4-BPS circular Wilson loops (a family of “latitudes”) in N=4 Super Yang-Mills theory, computing the one-loop corrections to the relevant classical string solutions in AdS5 ×S5. Supersymmetric localization provides an exact result that, in the large ’t Hooft coupling limit, should be reproduced by the sigma-model approach. To avoid ambiguities due to the absolute normalization of the string partition function, we compare the ratio between the generic latitude and the maximal 1/2-BPS circle: any measure-related ambiguity should simply cancel in this way. We use the Gel’fand-Yaglom method with Dirichlet boundary conditions to calculate the relevant functional determinants, that present some complications with respect to the standard circular case. After a careful numerical evaluation of our final expression we still find disagreement with the localization answer: the difference is encoded into a precise “remainder function”. We comment on the possible origin and resolution of this discordance
Remarks on the geometrical properties of semiclassically quantized strings
No full textWe discuss some geometrical aspects of the semiclassical quantization of string solutions in type IIB Green–Schwarz action on ADS5xS5 We concentrate on quadratic fluctuations around classical configurations, expressing the relevant differential operators in terms of (intrinsic and extrinsic) invariants of the background geometry. The aim of our exercise is to present some compact expressions encoding the spectral properties of bosonic and fermionic fluctuations. The appearing of non-trivial structures on the relevant bundles and their role in concrete computations are also considered. We corroborate the presentation of general formulas by working out explicitly a couple of relevant examples, namely the spinning string and the latitude BPS Wilson loop
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