We present a calculation of the four-loop anomalous dimension of the SU(2) sector Konishi operator in N=4 SYM, as an example of "wrapping" corrections to the known result for long operators. We use the known dilatation operator at four loops acting on long operator, and just calculate those diagrams which are affected by the change from operator length L > 4 to L = 4. We find that the answer involves a Zeta[5], so it has trancendentality degree five. Our result differs from previous proposals and calculations. We also discuss some ideas for extending this analysis to determine finite size corrections for operators of arbitrary length in the SU(2) sector.
We consider structure constants of single trace operators in planar $\mathcal{N}$ = 4 Super-Yang-Mills theory within the hexagon framework. The standard procedure for forming a three point function out of two hexagons develops divergences when the effects of virtual particles wrapping around the operators are taken into account. In this paper, we explain how to renormalize these divergences away and obtain definite predictions, at the leading wrapping order, for some of the structure constants that parameterize the OPE of two chiral primaries. We test our method at weak coupling against the fo…
We compute in this short note the OPE coefficient of two 20' operators and the Konishi. We use the OPE decomposition of a four point function of four 20' operators and the method of asymptotic expansions to compute the integrals at the order that it is needed.
We revisit the calculation of instanton effects in correlation functions in ${\cal N}=4$ SYM involving the Konishi operator and operators of twist two. Previous studies revealed that the scaling dimensions and the OPE coefficients of these operators do not receive instanton corrections in the semiclassical approximation. We go beyond this approximation and demonstrate that, while operators belonging to the same ${\cal N}=4$ supermultiplet ought to have the same conformal data, the evaluation of quantum instanton corrections for one operator can be mapped into a semiclassical computation for an…
Semiclassical string computation of strong-coupling corrections to dimensions of operators in Konishi multiplet
在arXiv：0906.4294中的工作之后，我们展示了如何使用半经典弦量子化方法来计算AdS_5 x S^5弦态在第一激发弦能级上的能量的主要修正，这些修正应该对应于N=4 SYM理论的Konishi多重态中的算子。与前一篇文章中的例子相比，我们在这里考虑的弦解带有S^5角动量J的额外分量，这便于它们与小西多重态中的算符相鉴别。我们证明，对于J=2的弦态，在能量的大弦张力展开中，子前导λ ^（-1/4）项的系数是arXiv：0906.4294中发现的系数的两倍。由此得到的值与Y系统/TBA方法在sl（2）扇区中为小西状态找到的值相匹配，解决了之前声称的明显分歧。
We use the method of asymptotic expansions to study the OPE limit of a four-point function of protected operators in N=4 SYM. We use a new method for evaluating the resulting propagator-type integrals and then extract the OPE coefficient with Konishi at the five loop order.
Quantum folded string in S^5 and the Konishi multiplet at strong coupling
小西超共形多重态是一个重要的理论实验室，人们可以在这里测试AdS/CFT方法，以计算对AdS_5 x S^5超弦谱的强耦合修正。特别地，可以利用有限电荷状态/算子的可积性。多重态基态是在N=4的超Yang-Mills理论的秩1扇区sl（2）和su（2）中具有两个简单后代的单重态算符。最近，对sl（2）态的次领先量子修正已经被计算出来。在这里，我们使用代数曲线的方法来确定对其他状态的校正，恢复多重态内校正的普适性。
The two-loop four-point amplitude of two massless SU(N) colored scalars and two color singlet operators with different virtuality described by a half-BPS and Konishi operators is calculated analytically in maximally supersymmetric Yang-Mills theory. We verify the ultraviolet behaviour of the unprotected composite operator and exponentiation of the infrared divergences with correct universal values of the anomalous dimensions in the modified dimensional reduction scheme. The amplitude is found to contain lower transcendental weight terms in addition to the highest ones and the latter has no sim…
We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in ${\cal N}=4$ supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction ($\overline {DR}$) scheme. We show that it satisfies KG equation in $\overline {DR}$ scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to …
We study the form factors of the Konishi operator, the prime example of non-protected operators in N=4 SYM theory, via the on-shell unitarity methods. Since the Konishi operator is not protected by supersymmetry, its form factors share many features with those in QCD, such as the occurrence of rational terms and of UV divergences that require renormalization. A subtle point is that this operator depends on the spacetime dimension. This requires a modification when calculating its form factors via unitarity methods. We derive a rigorous prescription that implements this modification to all loop…
We present three point form factors (FF) in ${\cal N}=4$ Super Yang Mills theory for both the half-BPS and the Konishi operators at two loop level in the `t Hooft coupling using Feynman diagrammatic approach. We have chosen on shell final states consisting of $g ϕϕ$ and $ϕλλ$, where $ϕ,λ, g$ are scalar, Majorana fermion and gauge fields respectively. The computation is done both in the modified dimensional reduction as well as in the four dimensional helicity scheme. We have studied the universal structure of infrared (IR) singularities in these FFs using Catani's IR subtraction operators. Exp…
We review some recent progress in understanding the spectrum of energies/dimensions of strings/operators in AdS5 x S5 -- planar N=4 super Yang-Mills correspondence. We consider leading strong coupling corrections to the energy of lightest massive string modes in AdS5 x S5, which should be dual to members of the Konishi operator multiplet in the SYM theory. This determines the general structure of strong-coupling expansion of the anomalous dimension of the Konishi operator. Following arXiv:0906.4294 we use 1-loop results for semiclassical string states to extract information about the leading c…
We present the calculation of the leading instanton contribution to the scaling dimensions of twist-two operators with arbitrary spin and to their structure constants in the OPE of two half-BPS operators in $\mathcal N=4$ SYM. For spin-two operators we verify that, in agreement with $\mathcal N=4$ superconformal Ward identities, the obtained expressions coincide with those for the Konishi operator. For operators with high spin we find that the leading instanton correction vanishes. This arises as the result of a rather involved calculation and requires a better understanding.
