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arXiv · 2610.13501

Integrable auxiliary field sigma model and the metric approach to $T\bar{T}$-like deformations

Nicola Baglioni·Daniele Bielli·Parita Shah·Gabriele Tartaglino-Mazzucchelli
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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 $T\bar{T}$-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 $T\bar{T}$ as the only deformation that can be interpreted as a field-dependent coordinate transformation.

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Nicola Baglioni, Daniele Bielli, Parita Shah, Gabriele Tartaglino-Mazzucchelli. 2026-10-09. Integrable auxiliary field sigma model and the metric approach to $T\bar{T}$-like deformations. https://arxiv.org/abs/2610.13501

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