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

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.

23 pages

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• Lifting at higher levels in the D1D5 CFT
• Lifting of level-1 states in the D1D5 CFT
• The OPE of bare twist operators in bosonic $S_N$ orbifold CFTs at large $N$
• Microstate Renormalization in Deformed D1-D5 SCFT
• Perturbing the symmetric orbifold from the worldsheet
• Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT${}_2$
• Lifting of states in 2-dimensional $N=4$ supersymmetric CFTs
• On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT
• Renormalization of Twisted Ramond Fields in D1-D5 SCFT${}_2$
• The large $N$ limit of OPEs in symmetric orbifold CFTs with $\mathcal{N}=(4,4)$ supersymmetry
• Dynamics of R-neutral Ramond fields in the D1-D5 SCFT
• Component twist method for higher twists in D1D5 CFT
• Thermalization in the D1D5 CFT
• Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$
• Dynamical evolution in the D1D5 CFT
• The Dual of a Tidal Force in the D1D5 CFT
• Larger Twists and Higher $n$-Point Functions with Fractional Conformal Descendants in $S_N$ Orbifold CFTs at Large $N$
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure