Operator mixing for string states in the D1-D5 CFT near the orbifold point

Abstract

In the context of the fuzzball programme, we investigate deforming the microscopic string description of the D1-D5 system on T^4xS^1 away from the orbifold point. Using conformal perturbation theory and a generalization of Lunin-Mathur symmetric orbifold technology for computing twist-nontwist correlators developed in a companion work, we initiate a program to compute the anomalous dimensions of low-lying string states in the D1-D5 superconformal field theory. Our method entails finding four-point functions involving a string operator O of interest and the deformation operator, taking coincidence limits to identify which other operators mix with O, subtracting the identified conformal family to isolate other contributions to the four-point function, finding the mixing coefficients, and iterating. For the lowest-lying string modes, this procedure should truncate in a finite number of steps. We check our method by showing how the operator dual to the dilaton does not participate in mixing that would change its conformal dimension, as expected. Next we complete the first stage of the iteration procedure for a low-lying string state of the form \partial X \partial X \bar\partial X \bar\partial X and find its mixing coefficient. Our main qualitative result is evidence of operator mixing at first order in the deformation parameter, which means that the string state acquires an anomalous dimension. After diagonalization this will mean that anomalous dimensions of some string states in the D1-D5 SCFT must decrease away from the orbifold point while others increase.

43 pages, added references and a comment

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Cited by in corpus (32)

• Entanglement Scrambling in 2d Conformal Field Theory
• The flaw in the firewall argument
• Lifting of D1-D5-P states
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• Bogoliubov coefficients for the twist operator in the D1D5 CFT
• Twist-nontwist correlators in M^N/S_N orbifold CFTs
• Analyzing the squeezed state generated by a twist deformation
• Lifting at higher levels in the D1D5 CFT
• Operator mixing in deformed D1D5 CFT and the OPE on the cover
• Beyond the Tensionless Limit: Integrability in the Symmetric Orbifold
• Lifting of level-1 states in the D1D5 CFT
• BPS Chaos
• Conformal Perturbation Theory for Twisted Fields
• Microstate Renormalization in Deformed D1-D5 SCFT
• Universal lifting in the D1-D5 CFT
• 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${}_2$
• Multi-centered D1-D5 solutions at finite B-moduli
• Dynamics of R-neutral Ramond fields in the D1-D5 SCFT
• Component twist method for higher twists in D1D5 CFT
• Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$
• Bosonization, cocycles, and the D1-D5 CFT on the covering surface
• Dynamical evolution in the D1D5 CFT
• Larger Twists and Higher $n$-Point Functions with Fractional Conformal Descendants in $S_N$ Orbifold CFTs at Large $N$
• Perturbed symmetric-product orbifold: first-order mixing and puzzles for integrability
• Pulsating strings from two dimensional CFT on $(T^4{)}^N/S(N)$
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• AdS3 Holography for 1/4 and 1/8 BPS geometries
• Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure