Tropical QFT and the sine-Gordon model
Abstract
A tropical quantum field theory is an exactly solvable deformation limit of an ordinary QFT, governed by a non-linear partial differential equation. We use the integrable two-dimensional sine-Gordon theory as a testbench to compare the exact features of an undeformed model with its tropical counterpart. We classify scale-invariant tropical QFTs in D=2 and leverage functional renormalization group methods to demonstrate that all scale-invariant theories with periodic effective actions are infrared fixed points of flows originating from sine-Gordon Lagrangians. For the tropical sine-Gordon model, we compute the β-functions exactly, solve the renormalized theory both via a convergent expansion and numerically for all admissible couplings, and illustrate the complete renormalization group flow from the Gaussian to the IR fixed point. Finally, we study the large-order behaviour of the loop expansion and relate it to the Hamilton-Jacobi equation, whose solutions we interpret as tropical instantons.
Related
- Form factors of field exponentials in the 1+1 dimensional Sine-Gordon model
- Wronskian representations of the solutions to the sine-Gordon equation
- Probabilistic ultraviolet renormalization of the two-dimensional Sine-Gordon model
- An integrable deformation of the sine(sinh)-Gordon model -- Non-Lie algebra
- Large number of hyperbolic and periodic solutions of sine-Gordon equation with nontrivial time dependence
BibTeX
@misc{borinsky2026tropical,
title = {{Tropical QFT and the sine-Gordon model}},
author = {Michael Borinsky and Jury Radkovski and Suriyah Rajalingam Kannagi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12653},
eprint = {2610.12653},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12653},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tropical QFT and the sine-Gordon model
AU - Michael Borinsky
AU - Jury Radkovski
AU - Suriyah Rajalingam Kannagi
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12653
UR - https://arxiv.org/abs/2610.12653
AB - A tropical quantum field theory is an exactly solvable deformation limit of an ordinary QFT, governed by a non-linear partial differential equation. We use the integrable two-dimensional sine-Gordon theory as a testbench to compare the exact features of an undeformed model with its tropical counterpart. We classify scale-invariant tropical QFTs in D=2 and leverage functional renormalization group methods to demonstrate that all scale-invariant theories with periodic effective actions are infrared fixed points of flows originating from sine-Gordon Lagrangians. For the tropical sine-Gordon model, we compute the β-functions exactly, solve the renormalized theory both via a convergent expansion and numerically for all admissible couplings, and illustrate the complete renormalization group flow from the Gaussian to the IR fixed point. Finally, we study the large-order behaviour of the loop expansion and relate it to the Hamilton-Jacobi equation, whose solutions we interpret as tropical instantons.
ER -