Operator mixing in deformed D1D5 CFT and the OPE on the cover

TL;DR

This paper develops a method using the OPE on the covering surface to compute operator mixing in the D1D5 CFT near the orbifold point, enabling more efficient calculations of structure constants and operator mixing.

Contribution

It introduces an OPE-based technique on the cover surface to analyze operator mixing and structure constants in the D1D5 CFT, including unprotected operators.

Findings

OPE on the cover encodes structure constants and mixing operators.

No first-order anomalous dimension shift for supergravity dual operators.

Correct structure constants obtained for dilaton and (2,2) operators.

Abstract

We consider the D1D5 CFT near the orbifold point and develop methods for computing the mixing of untwisted operators to first order by using the OPE on the covering surface. We argue that the OPE on the cover encodes both the structure constants for the orbifold CFT and the explicit form of the mixing operators. We show this explicitly for some example operators. We start by considering a family of operators dual to supergravity modes, and show that the OPE implies that there is no shift in the anomalous dimension to first order, as expected. We specialize to the operator dual to the dilaton, and show that the leading order singularity in the OPE reproduces the correct structure constant. Finally, we consider an unprotected operator of conformal dimension (2,2), and show that the leading order singularity and one of the subleading singularies both reproduce the correct structure constant. We check that the operator produced at subleading order using the OPE method is correct by calculating a number of three point functions using a Mathematica package we developed. Further development of this OPE technique should lead to more efficient calculations for the D1D5 CFT perturbed away from the orbifold point.