Integrability in gauge-gravity correspondence and gluon scattering amplitudes

在规范理论和弦理论中，可积性在获得解析的、精确的结果方面变得越来越重要。在这个研究项目中，我们澄清了规范理论和弦理论中的几个可积结构，并充分利用它们来获得解析结果。更具体地说，我们研究了四维最大超对称规范理论在强耦合条件下的胶子散射振幅。规范-重力对应关系将振幅与某些极小表面的面积联系起来。在此基础上，我们提出了一种利用二维共形场理论计算一般类胶子散射振幅的方法。我们还研究了E弦理论，它是六维中最简单的一致超对称场论之一。我们构造了E弦理论的BPS配分函数的封闭表达式，将其环面压缩到四维，并阐明了它的性质。

Integrability has become of increasing importance in obtaining analytic, exact results in gauge and string theories. In this research project we clarified several integrable structures in gauge and string theories and made full use of them to obtain analytic results. More specifically, we studied gluon scattering amplitudes at strong coupling in the maximally supersymmetric gauge theory in four dimensions. The gauge-gravity correspondence relates the amplitudes to the areas of certain minimal surfaces. Based on this correspondence we formulated a method of computing a general class of gluon scattering amplitudes by means of two-dimensional conformal field theories. We also studied the E-string theory, which is one of the simplest consistent supersymmetric field theories in six dimensions. We constructed a closed expression for the BPS partition function of the E-string theory toroidally compactified down to four dimensions and elucidated its properties.