Light non-vacuum BMS3 blocks at order 1/cM
Abstract
We derive a closed expression for the 1/cM correction to highest-weight BMS3 blocks with four light external primaries of generic weights and non-vacuum exchange. With cL and all operator weights held fixed, we prove that the global sector and descendants containing exactly one non-global generator L−n or M−n with n≥2 suffice through this order. This truncation reduces the intrinsic calculation to global blocks and their derivatives, whose contributions we resum for nonzero exchanged boost weight ξp. For pairwise identical external operators, we independently reproduce the correction through the introduction of boundary gravitons in the normalized three-point functions in the shadow representation, while keeping the exchanged two-point function fixed. The analogous prescription also reproduces the known non-vacuum Virasoro correction at order 1/c. For the same external configuration, a formal ultra-relativistic contraction of Virasoro blocks with one flipped chiral representation provides a further check: it yields the same correction, and we prove that contraction commutes with extraction of the 1/cM coefficient at each fixed descendant level. The degenerate exchange with ξp=0 requires a separate quotient construction and is not obtained as a smooth limit of the generic block, which we discuss in the appendix.
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BibTeX
@misc{yu2026light,
title = {{Light non-vacuum BMS$_3$ blocks at order $1/c_M$}},
author = {Boyang Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39893},
eprint = {2609.39893},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39893},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Light non-vacuum BMS_3 blocks at order 1/c_M
AU - Boyang Yu
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39893
UR - https://arxiv.org/abs/2609.39893
AB - We derive a closed expression for the 1/c_M correction to highest-weight BMS_3 blocks with four light external primaries of generic weights and non-vacuum exchange. With c_L and all operator weights held fixed, we prove that the global sector and descendants containing exactly one non-global generator L_−n or M_−n with n≥2 suffice through this order. This truncation reduces the intrinsic calculation to global blocks and their derivatives, whose contributions we resum for nonzero exchanged boost weight ξ_p. For pairwise identical external operators, we independently reproduce the correction through the introduction of boundary gravitons in the normalized three-point functions in the shadow representation, while keeping the exchanged two-point function fixed. The analogous prescription also reproduces the known non-vacuum Virasoro correction at order 1/c. For the same external configuration, a formal ultra-relativistic contraction of Virasoro blocks with one flipped chiral representation provides a further check: it yields the same correction, and we prove that contraction commutes with extraction of the 1/c_M coefficient at each fixed descendant level. The degenerate exchange with ξ_p=0 requires a separate quotient construction and is not obtained as a smooth limit of the generic block, which we discuss in the appendix.
ER -