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Algebra of the Infrared with Elliptic Curve-Valued Potential
Abstract
We study an extension of the algebra of the infrared to curve--valued potentials, focusing on the elliptic curve case. Given a finite configuration of points on an elliptic curve, we construct associated L∞-algebra. Adding an extra point produces a directed A∞-algebra and an L∞-morphism to their directed Hochschild deformation complexes. Maurer--Cartan elements of the L∞-algebra determine A∞-deformations of the directed algebra. We formulate a conjectural comparison between Maurer--Cartan deformations of the directed algebra and the directed Fukaya--Seidel category associated to compatible finite collections of thimbles.
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BibTeX
@misc{li2026algebra,
title = {{Algebra of the Infrared with Elliptic Curve-Valued Potential}},
author = {Longfei Li},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.04039},
eprint = {2607.04039},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04039},
}
RIS
TY - UNPB
TI - Algebra of the Infrared with Elliptic Curve-Valued Potential
AU - Longfei Li
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2607.04039
UR - https://arxiv.org/abs/2607.04039
AB - We study an extension of the algebra of the infrared to curve--valued potentials, focusing on the elliptic curve case. Given a finite configuration of points on an elliptic curve, we construct associated L_∞-algebra. Adding an extra point produces a directed A_∞-algebra and an L_∞-morphism to their directed Hochschild deformation complexes. Maurer--Cartan elements of the L_∞-algebra determine A_∞-deformations of the directed algebra. We formulate a conjectural comparison between Maurer--Cartan deformations of the directed algebra and the directed Fukaya--Seidel category associated to compatible finite collections of thimbles.
ER -