Integrable auxiliary field sigma model and the metric approach to TT̅-like deformations
Abstract
We describe a family of two-dimensional metric deformations that preserve integrability. The seeds are (classically) conformal integrable field theories and the deformations are directly related to different classes of auxiliary field sigma models. We introduce a master action connecting deformations by Lie-algebra-valued auxiliary fields, the so-called ν-frame, to deformations by two Lorentz-charged scalars. These auxiliary scalar fields can be identified as Beltrami differentials of an auxiliary two-dimensional metric, providing a direct connection with the metric approach to TT̅-like deformations. For Weyl-invariant seed matter theories, the auxiliary metric sector is described by a reduced gravitational potential. We show that the resulting framework preserves classical Lax integrability whenever the seed matter theory admits a Lax representation of its equations of motion on a generic curved two-dimensional spacetime. Finally, within the Lorentz-invariant family and the zweibein deformations of conformal matter theories considered here, we identify TT̅ as the only deformation that can be interpreted as a field-dependent coordinate transformation.
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BibTeX
@misc{baglioni2026integrable,
title = {{Integrable auxiliary field sigma model and the metric approach to $T\barT$-like deformations}},
author = {Nicola Baglioni and Daniele Bielli and Parita Shah and Gabriele Tartaglino-Mazzucchelli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13501},
eprint = {2610.13501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13501},
}
RIS
TY - UNPB
TI - Integrable auxiliary field sigma model and the metric approach to TT̅-like deformations
AU - Nicola Baglioni
AU - Daniele Bielli
AU - Parita Shah
AU - Gabriele Tartaglino-Mazzucchelli
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13501
UR - https://arxiv.org/abs/2610.13501
AB - We describe a family of two-dimensional metric deformations that preserve integrability. The seeds are (classically) conformal integrable field theories and the deformations are directly related to different classes of auxiliary field sigma models. We introduce a master action connecting deformations by Lie-algebra-valued auxiliary fields, the so-called ν-frame, to deformations by two Lorentz-charged scalars. These auxiliary scalar fields can be identified as Beltrami differentials of an auxiliary two-dimensional metric, providing a direct connection with the metric approach to TT̅-like deformations. For Weyl-invariant seed matter theories, the auxiliary metric sector is described by a reduced gravitational potential. We show that the resulting framework preserves classical Lax integrability whenever the seed matter theory admits a Lax representation of its equations of motion on a generic curved two-dimensional spacetime. Finally, within the Lorentz-invariant family and the zweibein deformations of conformal matter theories considered here, we identify TT̅ as the only deformation that can be interpreted as a field-dependent coordinate transformation.
ER -