Holography for integrable field theories
Abstract
We develop a holographic dual to the integrable field theories built from 4d Chern-Simons theory. The dual theory is a topological string on a generalized Calabi-Yau manifold, which is entirely encoded in a geometric object we call a planar spectral curve. We describe the RG flow for a planar integrable field theory as a geometric flow on the moduli of planar spectral curves. This description is valid at all orders in the 't Hooft coupling. We compute this flow explicitly up to two loops in many examples, and find an exact match with known field theory results. At one loop this includes a wide class of models. At two loops we reproduce the RG flow for the principal chiral model with WZ term, and for a class of integrable σ-models with target U(N) × U(N).
Related
- Time-dependent integrable quantum field theories with dynamical boundaries
- Quasi-Normal Modes and thermalization in integrable Quantum Field Theories from the Thermodynamic Bethe Ansatz
- Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions
- Elliptic spin Ruijsenaars-Schneider integrable models from 5d 𝒩=1 gauge theories
- Integrable auxiliary field sigma model and the metric approach to TT̅-like deformations
BibTeX
@misc{costello2026holography,
title = {{Holography for integrable field theories}},
author = {Kevin Costello and Joaquin Liniado},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34909},
eprint = {2609.34909},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34909},
}
RIS
TY - UNPB
TI - Holography for integrable field theories
AU - Kevin Costello
AU - Joaquin Liniado
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34909
UR - https://arxiv.org/abs/2609.34909
AB - We develop a holographic dual to the integrable field theories built from 4d Chern-Simons theory. The dual theory is a topological string on a generalized Calabi-Yau manifold, which is entirely encoded in a geometric object we call a planar spectral curve. We describe the RG flow for a planar integrable field theory as a geometric flow on the moduli of planar spectral curves. This description is valid at all orders in the 't Hooft coupling. We compute this flow explicitly up to two loops in many examples, and find an exact match with known field theory results. At one loop this includes a wide class of models. At two loops we reproduce the RG flow for the principal chiral model with WZ term, and for a class of integrable σ-models with target U(N) × U(N).
ER -