Core Concepts
The authors show that for a certain solution subspace of two-dimensional gravitational models obtained by dimensional reduction of four-dimensional gravity theories with a cosmological constant, a subset of the equations of motion can be viewed as the compatibility conditions of a modified version of the Breitenlohner-Maison linear system. They also employ machine learning techniques to identify Lax pair matrices for the one-dimensional description of these integrable models.
Abstract
The content discusses the integrability properties of two-dimensional gravitational models obtained by dimensional reduction of four-dimensional gravity theories in the presence of a cosmological constant.
Key highlights:
- In the absence of a cosmological constant, the dimensionally reduced two-dimensional models are known to be classically integrable, with their equations of motion being the compatibility conditions of the Breitenlohner-Maison (BM) linear system.
- When a cosmological constant is introduced, the integrability of the dimensionally reduced models is generally lost.
- However, the authors identify a specific solution subspace for which a subset of the two-dimensional equations of motion can still be viewed as the compatibility conditions of a modified version of the BM linear system.
- For this solution subspace, the authors provide a one-dimensional description and discuss its Liouville integrability.
- They employ machine learning techniques, specifically a linear neural network, to search for Lax pair matrices that characterize the integrability of the one-dimensional systems.
- The machine learning approach is shown to be effective in identifying integrable structures in these classical systems.
Stats
The authors do not provide any specific numerical data or statistics in the content. The focus is on the analytical and machine learning results related to the integrability of the dimensionally reduced gravitational models.
Quotes
"We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the presence of a potential for the neutral scalar fields."
"Here, we show that in the presence of a scalar potential, for a certain solution subspace, a subset of the equations of motion in two dimensions can still be viewed as being the compatibility conditions of a linear system, namely a modified version of the BM linear system."
"We illustrate the search for Lax pair matrices in specific models using both analytic and ML techniques. Our ML experiments suggest conserved currents that help determine Lax pairs for the models under consideration."