Abstract
We study the operator product expansion (OPE) of two identical scalar primary operators in the lightcone limit in a conformal field theory where a scalar is the operator with lowest twist. We see that in CFTs where both the stress tensor and a scalar are the lowest twist operators, the stress tensor contributes at the leading order in the lightcone OPE and the scalar contributes at the subleading order. We also see that there does not exist a scalar analogue of the average null energy condition (ANEC) for a CFT where a scalar is the lowest twist operator.
Highlights
The operator product expansion (OPE) is used often in nonperturbative studies of quantum field theories
We have studied the light-cone OPE in a unitary conformal field theory (CFT) where the lowest twist operator is a scalar primary operator
We show that in such cases the stress tensor contributes to the light-cone OPE at leading order, whereas the scalar primary contributes at the subleading order
Summary
The operator product expansion (OPE) is used often in nonperturbative studies of quantum field theories. We study the N 1⁄4 4 supersymmetric Yang-Mills theory in d 1⁄4 4 which has both the stress tensor and a scalar primary as lowest twist operators. If a CFT has the stress tensor to be the lowest twist operator, in the v → 0 limit, the leading order contribution in the OPE comes from the following components of the stress tensor and its descendants, Tuu; ∂uTuu; ∂2uTuu;. This allows us to write the light-cone OPE in the following summation form:
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