Breakdown of the operator product expansion in the 't Hooft model

TL;DR

This paper investigates deep inelastic scattering in the solvable 't Hooft model, revealing a discrepancy in the operator product expansion related to non-local operators, with implications for four-dimensional theories.

Contribution

It demonstrates a mismatch in the operator product expansion in the 't Hooft model, highlighting the role of non-local operators and suggesting similar effects in four-dimensional large N_c theories.

Findings

Matching moments in both computations except for one involving non-local operators

Identification of a potential breakdown of local OPE in the model

Implication that similar phenomena may occur in 4D large N_c QCD

Abstract

We consider deep inelastic scattering in the 't Hooft model. Being solvable, this model allows us to directly compute the moments associated with the cross section at next-to-leading order in the 1/Q^2 expansion. We perform the same computation using the operator product expansion. We find that all the terms match in both computations except for one in the hadronic side, which is proportional to a non-local operator. The basics of the result suggest that a similar phenomenon may occur in four dimensions in the large N_c limit.