Abstract
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.
Highlights
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 N = 4 SYM
In [8] we argued that, by virtue of N = 4 superconformal symmetry, the above mentioned instanton effects can be determined from the semiclassical computation of two- and three-point correlation functions for another operator in the same supermultiplet
For S ≥ 4, quite surprisingly, our calculation yields a vanishing result for the instanton contribution. This implies that the leading instanton corrections to the conformal data of twist-two operators OS with S ≥ 4 are suppressed at least by a power of g2 as compared with those for the Konishi operator
Summary
All twist-two operators in N = 4 SYM belong to the same supermultiplet and share the same conformal data. Coefficients are fixed by the condition for OS(x) to be a conformal primary operator and depend, in general, on the coupling constant. YAB is introduced to project the product of two scalar fields onto the representation 20 of the SU(4) R−symmetry group. It satisfies ABCDYABYCD = 0 and plays the role of the coordinate of the operator in the isotopic SU(4) space. The scaling dimension of twist-two operator ∆S, the normalization factor NS and three-point coefficient function CS depend on the coupling constant whereas the scaling dimension of the half-BPS operator is protected from quantum corrections
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