Fine structure of anomalous dimensions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math>super-Yang–Mills theory

We consider higher spin operators in weakly coupled gauge conformal field theories. Crossing symmetry of mixed scalar correlators relates different higher spin towers and we study the consequences for the spectrum and structure constants of higher spin operators of different twists. Constraints are obtained to all loops in perturbation theory. The large spin contributions to the structure constants can be resummed into a theorydependent prefactor times a universal factor, whose structure of poles agrees with the one that would be obtained from a Witten diagram supergravity computation, although only crossing symmetry is assumed. Finally, our results provide an all loop expression for the double null limit of mixed correlators, which is in perfect agreement with the correlator/Wilson loop correspondence.

“…and so on. This is consistent with the analysis of [13]. Note that due to degeneracy in general γ 2 = γ 2 .…”

Section: Solving the Integral Equationsupporting

confidence: 91%

Section: Twistmentioning

confidence: 88%

Section: Solving the Integral Equationmentioning

confidence: 91%

See 1 more Smart Citation

Crossing symmetry and Higher spin towers

Alday

Bissi

2017

“…In the limit x → 1 the diagonal terms in the splitting functions, P qq and P gg , feature divergent contributions [46,[101][102][103], namely…”

Section: Perturbative Calculation At Large Xmentioning

confidence: 99%

Relating amplitude and PDF factorisation through Wilson-line geometries

Falcioni

Gardi

Milloy

2019

We study long-distance singularities governing different physical quantities involving massless partons in perturbative QCD by using factorisation in terms of Wilson-line correlators. By isolating the process-independent hard-collinear singularities from quark and gluon form factors, and identifying these with the ones governing the elastic limit of the perturbative Parton Distribution Functions (PDFs)δ(1 − x) in the large-x limit of DGLAP splitting functions -we extract the anomalous dimension controlling soft singularities of the PDFs, verifying that it admits Casimir scaling. We then perform an independent diagrammatic computation of the latter using its definition in terms of Wilson lines, confirming explicitly the above result through two loops. By comparing our eikonal PDF calculation to that of the eikonal form factor by Erdogan and Sterman and the classical computation of the closed parallelogram by Korchemsky and Korchemskaya, a consistent picture emerges whereby all singularities emerge in diagrammatic configurations localised at the cusps or along lightlike lines, but where distinct contributions to the anomalous dimensions are associated with finite (closed) lightlike segments as compared to infinite (open) ones. Both are relevant for resumming large logarithms in physical quantities, notably the anomalous dimension controlling Drell-Yan or Higgs production near threshold on the one hand, and the gluon Regge trajectory controlling the high-energy limit of partonic scattering on the other. Isolating hard-collinear singularitiesThe contribution of Γ J in eq. (2.18) is associated to the soft singularities of J i , which cancel in the ratio of J i and J i eq. (2.9). It is therefore convenient to focus on the poles of pure hard-collinear origin, defined aswhere J i | pole means only the poles of the jet function. We extract the function J i/J for i = q and i = g from the form factor of the quark and of the gluon, respectively, thus providing the process-independent components containing the purely collinear singularities associated with massless external partons. In order to determine J i/J , we isolate the pole part of the jet function J i , by replacing in eq. (2.18) the function G(1, α s , ǫ) with γ G , according to the

“…The anomalous dimension of these operators occupy a band [3]. A distinguished sub-set among these is formed by the ground states, i.e.…”

Section: Introductionmentioning

confidence: 99%

From weak coupling to spinning strings

Freyhult

Rej

Zieme

2010

We identify the gauge theory dual of a spinning string of minimal energy with spins S 1 , S 2 on AdS 5 and charge J on S 5 . For this purpose we focus on a certain set of local operators with two different types of covariant derivatives acting on complex scalar fields. We analyse the corresponding nested Bethe equations for the ground states in the limit of large spins. The auxiliary Bethe roots form certain string configurations in the complex plane, which enable us to derive integral equations for the leading and subleading contribution to the anomalous dimension. The results can be expressed through the observables of the sl(2) sub-sector, i.e. the cusp anomaly f (g) and the virtual scaling function B L (g), rendering the strong-coupling analysis straightforward. Furthermore, we also study a particular sub-class of these operators specialising to a scaling limit with finite values of the second spin at weak and strong coupling.