Spectral flow in AdS3 revisited
Abstract
We revisit an old idea that spectral flow in WZW models can be associated with certain G-bundles over a worldsheet. This allows us to introduce a novel method for computing correlators of spectrally-flowed vertex operators in WZW models with group G and level k, by systematically computing the contribution from a network of line defects. Specialising to the case of G=SL(2, ℝ), as is relevant to AdS3 string theory, we demonstrate that generic n-point functions of spectrally-flowed vertex operators at tree level can be rewritten in terms of an (n+1)-point function of n unflowed vertex operators and one degenerate insertion. This is to be interpreted as an unflowed n-point function in an instanton background. Moreover, we conjecture that this (n+1)-point function can be recast as an n-point function of unflowed operators and we provide evidence for this. We demonstrate that the (n+1)-point function satisfies the same constraints from global spacetime conformal invariance as does an unflowed n-point function for a specific choice of spacetime coordinates that we determine. We verify that our results agree with bootstrap results in the literature. This provides the next step towards fully solving the SL(2,ℝ) WZW model.
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BibTeX
@misc{mcstay2026spectral,
title = {{Spectral flow in AdS$\mathbf_3$ revisited}},
author = {Nathan McStay and Ronald Reid-Edwards and Sean Seet},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06295},
eprint = {2611.06295},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06295},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectral flow in AdS_3 revisited
AU - Nathan McStay
AU - Ronald Reid-Edwards
AU - Sean Seet
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06295
UR - https://arxiv.org/abs/2611.06295
AB - We revisit an old idea that spectral flow in WZW models can be associated with certain G-bundles over a worldsheet. This allows us to introduce a novel method for computing correlators of spectrally-flowed vertex operators in WZW models with group G and level k, by systematically computing the contribution from a network of line defects. Specialising to the case of G=SL(2, ℝ), as is relevant to AdS_3 string theory, we demonstrate that generic n-point functions of spectrally-flowed vertex operators at tree level can be rewritten in terms of an (n+1)-point function of n unflowed vertex operators and one degenerate insertion. This is to be interpreted as an unflowed n-point function in an instanton background. Moreover, we conjecture that this (n+1)-point function can be recast as an n-point function of unflowed operators and we provide evidence for this. We demonstrate that the (n+1)-point function satisfies the same constraints from global spacetime conformal invariance as does an unflowed n-point function for a specific choice of spacetime coordinates that we determine. We verify that our results agree with bootstrap results in the literature. This provides the next step towards fully solving the SL(2,ℝ) WZW model.
ER -