The Gaiotto-Kim Trace Formula and Line Defects
Abstract
We study the insertion of 4d half-BPS line defects into the trace formula proposed by Gaiotto and Kim, which computes the ellipsoid partition function of the 3d topological quantum field theory (TQFT) arising from a 4d 𝒩=2 superconformal field theory. This yields a homomorphism to 3d Wilson loops, preserving the fusion algebra of the 4d defects. We also present a systematic algorithm for determining the simple objects of a 3d TQFT in terms of Wilson loops in the UV 3d 𝒩=2 abelian Chern-Simons-matter theory. Utilizing supersymmetric localization, we characterize the modular S- and T-matrices of the TQFT. We apply our algorithm to various 3d TQFTs arising from the trace formula with higher-power monodromy of the (A1,G) Argyres-Douglas theories.
Related
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BibTeX
@misc{kim2026gaiottokim,
title = {{The Gaiotto-Kim Trace Formula and Line Defects}},
author = {Sungjoon Kim and Spencer Stubbs},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24582},
eprint = {2609.24582},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24582},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Gaiotto-Kim Trace Formula and Line Defects
AU - Sungjoon Kim
AU - Spencer Stubbs
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24582
UR - https://arxiv.org/abs/2609.24582
AB - We study the insertion of 4d half-BPS line defects into the trace formula proposed by Gaiotto and Kim, which computes the ellipsoid partition function of the 3d topological quantum field theory (TQFT) arising from a 4d 𝒩=2 superconformal field theory. This yields a homomorphism to 3d Wilson loops, preserving the fusion algebra of the 4d defects. We also present a systematic algorithm for determining the simple objects of a 3d TQFT in terms of Wilson loops in the UV 3d 𝒩=2 abelian Chern-Simons-matter theory. Utilizing supersymmetric localization, we characterize the modular S- and T-matrices of the TQFT. We apply our algorithm to various 3d TQFTs arising from the trace formula with higher-power monodromy of the (A_1,G) Argyres-Douglas theories.
ER -