AI 中文总结
研究如何从四维陈-西蒙斯理论构建含时可积系统，通过推广该理论，给出生成此类系统的方法，建立时间依赖与重整化群流的关系，此方法适用于多种理论并拓展了可积系统类别。
AI 中文摘要
可解的含时系统为研究非平衡物理提供重要背景，本文表明四维陈 - 西蒙斯理论为构建此类系统提供自然统一框架。通过推广该理论，给出生成含时可积场论的系统程序，建立普遍关系，这些理论保持拉克斯可积性且可用逆散射方法求解，还可改写为耦合物质的伸缩子引力。
英文摘要
Solvable time-dependent systems provide important settings for studying non-equilibrium physics, where exact results are rare. They are also useful for benchmarking quantum simulations, which can directly probe real-time dynamics beyond the reach of conventional numerical approaches. In this paper, we show that the four-dimensional Chern-Simons theory offers a natural and unifying framework for constructing such systems. Focusing on classically integrable field theories, we consider a generalization of the four-dimensional Chern-Simons theory in which the usual holomorphic one-form is replaced by a more general, spacetime-dependent one-form. This yields a systematic procedure for generating time-dependent integrable field theories and establishes a universal relation: for every theory obtained in this way, the allowed time dependence coincides with the one-loop renormalization group flow. Despite the explicit time dependence, these theories retain Lax integrability and remain solvable by inverse scattering methods. Our construction applies to both ultralocal and non-ultralocal theories and extends previously known time-dependent sigma models to a much broader class of integrable systems. It also admits rewriting as dilaton gravity coupled to matter, producing a large family of classically integrable dilaton gravity theories in two dimensions. We also comment on connections to time-dependent integrable models studied recently in condensed matter physics and non-autonomous integrable systems arising from dimensionally-reduced Einstein gravity.
Comments7 figures, 63 pages + appendices
