论文标题
可集成系统的扭曲器动作
Twistor Actions for Integrable Systems
论文作者
论文摘要
许多可集成的系统可以重新构成扭曲空间上的全态矢量束。这是整合系统理论中的强大组织原则。一个缺点是它是在运动方程级别配制的。从这个角度来看，综合系统具有Lagrangians是神秘的。在本文中，我们研究了Chern-Simons对Twistor空间的作用，并使用它来得出某些可集成的Sigma模型的Lagrangians。我们的重点是来自尺寸降低的重力和超级重力的示例。对两个时空维度的一般相对性的尺寸降低是与DILATON和2D重力耦合的可集成的coset Sigma模型。将超级重力降低到两个时空维度的维度降低是与物质费米子，dilaton和2D超级重力结合的可集成的coset sigma模型。我们使用Chern-Simons理论为这些2D集成系统得出了Lax运算符和Lagrangians。在超级示例中，我们使用了扩展的设置，其中扭曲的Chern-Simons理论与一对物质费米子结合在一起。
Many integrable systems can be reformulated as holomorphic vector bundles on twistor space. This is a powerful organizing principle in the theory of integrable systems. One shortcoming is that it is formulated at the level of the equations of motion. From this perspective, it is mysterious that integrable systems have Lagrangians. In this paper, we study a Chern-Simons action on twistor space and use it to derive the Lagrangians of some integrable sigma models. Our focus is on examples that come from dimensionally reduced gravity and supergravity. The dimensional reduction of general relativity to two spacetime dimensions is an integrable coset sigma model coupled to a dilaton and 2d gravity. The dimensional reduction of supergravity to two spacetime dimensions is an integrable coset sigma model coupled to matter fermions, a dilaton, and 2d supergravity. We derive Lax operators and Lagrangians for these 2d integrable systems using the Chern-Simons theory on twistor space. In the supergravity example, we use an extended setup in which twistor Chern-Simons theory is coupled to a pair of matter fermions.
