Auxiliary Field Deformations of the Lambda Model

Abstract

Many examples of integrable sigma models admit families of integrable deformations that involve coupling the undeformed ``seed'' theory to auxiliary fields with algebraic equations of motion. In this work, we apply this paradigm to the case where the seed theory is the lambda model, which interpolates between the Wess-Zumino-Witten model and the non-Abelian T-dual of the principal chiral model. We present an auxiliary field deformation of the lambda model and exhibit a Lax connection whose flatness is equivalent to the remaining equations of motion after imposing the algebraic field equations. We also carry out a Hamiltonian analysis of the deformed theory, verifying that it obeys the assumptions of theorems in arXiv:2605.18213 which guarantee both (i) that the model enjoys the Maillet structure that ensures involution of its conserved charges, and (ii) that the theory possesses a classical Yangian. Thus, as in other cases, the auxiliary field deformation of the lambda model changes its classical dynamics while leaving the integrable structure essentially unchanged.

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Cite

BibTeX RIS

BibTeX

@misc{ferko2026auxiliary,
  title = {{Auxiliary Field Deformations of the Lambda Model}},
  author = {Christian Ferko and Cian Luke Martin and Pranat Sharma},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18831},
  eprint = {2609.18831},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18831},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Auxiliary Field Deformations of the Lambda Model
AU  - Christian Ferko
AU  - Cian Luke Martin
AU  - Pranat Sharma
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18831
UR  - https://arxiv.org/abs/2609.18831
AB  - Many examples of integrable sigma models admit families of integrable deformations that involve coupling the undeformed ``seed'' theory to auxiliary fields with algebraic equations of motion. In this work, we apply this paradigm to the case where the seed theory is the lambda model, which interpolates between the Wess-Zumino-Witten model and the non-Abelian T-dual of the principal chiral model. We present an auxiliary field deformation of the lambda model and exhibit a Lax connection whose flatness is equivalent to the remaining equations of motion after imposing the algebraic field equations. We also carry out a Hamiltonian analysis of the deformed theory, verifying that it obeys the assumptions of theorems in arXiv:2605.18213 which guarantee both (i) that the model enjoys the Maillet structure that ensures involution of its conserved charges, and (ii) that the theory possesses a classical Yangian. Thus, as in other cases, the auxiliary field deformation of the lambda model changes its classical dynamics while leaving the integrable structure essentially unchanged.
ER  -

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