Computational homological methods for integrable field theories
Abstract
We develop explicit computational tools for the recent homological approach to the construction of -dimensional integrable field theories on from -dimensional semi-holomorphic Chern-Simons theory on . In this framework, the operation of integrating out the spectral curve is realized by homotopy transfer of a cyclic -algebra associated with the -dimensional theory with prescribed singularities and boundary conditions. We construct explicit strong deformation retracts for divisor-twisted Dolbeault complexes on and use them to make the transferred -structure computationally accessible. As an application, we study the choice of meromorphic -form corresponding to the principal chiral model with a Wess-Zumino term. We compute the transferred Maurer-Cartan action and the associated Lax connection, showing that the former resums to the standard principal chiral model action with a Wess-Zumino term and that the latter reproduces the usual Lax connection.
Cite
@article{arxiv.2607.12142,
title = {Computational homological methods for integrable field theories},
author = {Marco Benini and Ryan A. Cullinan and Alexander Schenkel and Benoit Vicedo},
journal= {arXiv preprint arXiv:2607.12142},
year = {2026}
}