English

Computational homological methods for integrable field theories

High Energy Physics - Theory 2026-07-13 v1 Mathematical Physics

Abstract

We develop explicit computational tools for the recent homological approach to the construction of 22-dimensional integrable field theories on Σ\Sigma from 44-dimensional semi-holomorphic Chern-Simons theory on Σ×C\Sigma \times C. In this framework, the operation of integrating out the spectral curve CC is realized by homotopy transfer of a cyclic LL_\infty-algebra associated with the 44-dimensional theory with prescribed singularities and boundary conditions. We construct explicit strong deformation retracts for divisor-twisted Dolbeault complexes on C=CP1C=\mathbb{C}P^1 and use them to make the transferred LL_\infty-structure computationally accessible. As an application, we study the choice of meromorphic 11-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}
}