Knizhnik-Zamolodchikov equations and the analytic structure of strings in AdS3
Abstract
The pole structure of string correlators in AdS3 encodes essential information about the AdS3/CFT2 duality. The corresponding residues for spectrally flowed three-point functions have been extracted from their exact expressions and shown to match the predictions of the holographic CFT. Away from the tensionless point, the latter is defined perturbatively in terms of a deformed symmetric orbifold. For n-point functions, such a matching has so far only been achieved for a specific subset of poles, and only by means of free-field techniques. Here we develop an alternative approach. We show that, starting from the localization properties of worldsheet correlators, one can solve the Knizhnik--Zamolodchikov (KZ) equations on the corresponding locus and perform the integration over worldsheet moduli explicitly for any n and for arbitrary values of the spectral flow charges. In this way we reproduce, directly from the exact worldsheet theory and including the normalization, the residues previously obtained with free-field methods. We expect this to provide a systematic framework for computing the remaining residues and, ultimately, for determining the full analytic structure of string amplitudes in AdS3.
Related
- Boundary Quantum Knizhnik-Zamolodchikov Equations and Integrability of Quantum Field Theories with Time-Dependent Bulk and Boundary Coupling Strengths
- Pre-Strings Lectures on Holographic Correlators and Analytic Bootstrap
- Bogomol'nyi equations for Kruglov strings
- Analytic solutions for the gravitational spin Hall equations and black hole shadows
- Equations of state of hydrodynamic type and particle statistics of a Dyson gas in an analytic confining potential
BibTeX
@misc{iguri2026knizhnikzamolodchikov,
title = {{Knizhnik-Zamolodchikov equations and the analytic structure of strings in AdS$_3$}},
author = {Sergio Iguri and Nicolas Kovensky and Julian H. Toro},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35495},
eprint = {2609.35495},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35495},
}
RIS
TY - UNPB
TI - Knizhnik-Zamolodchikov equations and the analytic structure of strings in AdS_3
AU - Sergio Iguri
AU - Nicolas Kovensky
AU - Julian H. Toro
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35495
UR - https://arxiv.org/abs/2609.35495
AB - The pole structure of string correlators in AdS_3 encodes essential information about the AdS_3/CFT_2 duality. The corresponding residues for spectrally flowed three-point functions have been extracted from their exact expressions and shown to match the predictions of the holographic CFT. Away from the tensionless point, the latter is defined perturbatively in terms of a deformed symmetric orbifold. For n-point functions, such a matching has so far only been achieved for a specific subset of poles, and only by means of free-field techniques. Here we develop an alternative approach. We show that, starting from the localization properties of worldsheet correlators, one can solve the Knizhnik--Zamolodchikov (KZ) equations on the corresponding locus and perform the integration over worldsheet moduli explicitly for any n and for arbitrary values of the spectral flow charges. In this way we reproduce, directly from the exact worldsheet theory and including the normalization, the residues previously obtained with free-field methods. We expect this to provide a systematic framework for computing the remaining residues and, ultimately, for determining the full analytic structure of string amplitudes in AdS_3.
ER -