Exact stress-tensor generators distinguish integrable continuations
Abstract
The same leading TT̅ interaction can coexist with sharply different strong-field responses, even within causal, classically integrable sigma models. We reconstruct exact autonomous stress-tensor generators for prescribed one-scale Courant--Hilbert families in two dimensions. Separating the invariant stress scale from a signed trace ratio reduces reconstruction to one scalar inversion on each invertible physical branch. The resulting profile determines both the deformation law and the relation between local energy density and pressure. For generalized Born--Infeld and logarithmic models, the leading interactions coincide, yet pressure saturates in the former and grows without bound in the latter. Their exact generators are respectively quadratic and nonpolynomial, the latter involving Lambert W−1. A regular Legendre transformation gives the same profile in the auxiliary potential formulation. The flows commute locally with root-TT̅ within a common smooth branch and retain a common classical Lax form. Exact reconstruction thus quantifies the nonlinear freedom left by leading-order matching.
Related
- Integrable Generators of Polynomial Vector Fields for Complex Classical Lie Groups
- The \textsc{ABC}-equation revisited: missed integrable cases. Part I: classification and (quasi) integrable structures
- ACC for lc thresholds for algebraically integrable foliations
- Flexibility of two-dimensional Euler flows with integrable vorticity
- Stability and instability of torus-symmetric Einstein spacetimes with square-integrable connection
BibTeX
@misc{babaeiaghbolagh2026exact,
title = {{Exact stress-tensor generators distinguish integrable continuations}},
author = {H. Babaei-Aghbolagh and Song He and Zahra Pezhman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31297},
eprint = {2610.31297},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31297},
}
RIS
TY - UNPB
TI - Exact stress-tensor generators distinguish integrable continuations
AU - H. Babaei-Aghbolagh
AU - Song He
AU - Zahra Pezhman
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31297
UR - https://arxiv.org/abs/2610.31297
AB - The same leading TT̅ interaction can coexist with sharply different strong-field responses, even within causal, classically integrable sigma models. We reconstruct exact autonomous stress-tensor generators for prescribed one-scale Courant--Hilbert families in two dimensions. Separating the invariant stress scale from a signed trace ratio reduces reconstruction to one scalar inversion on each invertible physical branch. The resulting profile determines both the deformation law and the relation between local energy density and pressure. For generalized Born--Infeld and logarithmic models, the leading interactions coincide, yet pressure saturates in the former and grows without bound in the latter. Their exact generators are respectively quadratic and nonpolynomial, the latter involving Lambert W_−1. A regular Legendre transformation gives the same profile in the auxiliary potential formulation. The flows commute locally with root-TT̅ within a common smooth branch and retain a common classical Lax form. Exact reconstruction thus quantifies the nonlinear freedom left by leading-order matching.
ER -