Integrable boundary interaction in 3D target space: the "pillow-brane" model

TL;DR

This paper introduces an integrable boundary interaction model in three-dimensional space where boundary fields are constrained on a pillow-shaped surface, proposing an exact solution via linear differential equations.

Contribution

It presents a novel integrable boundary interaction model in 3D target space with a unique pillow-shaped boundary constraint, and suggests an exact solution method.

Findings

Model is integrable with boundary fields on a pillow-shaped surface.

Exact solution is proposed using linear ordinary differential equations.

The model extends understanding of boundary interactions in higher-dimensional field theories.

Abstract

We propose a model of boundary interaction, with three-dimensional target space, and the boundary values of the field {\vec X}\in R^3 constrained to lay on a two-dimensional surface of the "pillow" shape. We argue that the model is integrable, and suggest that its exact solution is described in terms of certain linear ordinary differential equation.