Motivated by the desire to understand chaos in the S-matrix of string theory, we study tree level scattering amplitudes involving highly excited strings. While the amplitudes for scattering of light strings have been a hallmark of string theory since its early days, scattering of excited strings has been far less studied. Recent results on black hole chaos, combined with the correspondence principle between black holes and strings, suggest that the amplitudes have a rich structure. We review the procedure by which an excited string is formed by repeatedly scattering photons off of an initial tachyon (the DDF formalism). We compute the scattering amplitude of one arbitrary excited string and any number of tachyons in bosonic string theory. At high energies and high mass excited state these amplitudes are determined by a saddle-point in the integration over the positions of the string vertex operators on the sphere (or the upper half plane), thus yielding a generalization of the “scattering equations”. We find a compact expression for the amplitude of an excited string decaying into two tachyons, and study its properties for a generic excited string. We find the amplitude is highly erratic as a function of both the precise excited string state and of the tachyon scattering angle relative to its polarization, a sign of chaos.

渴望理解S中的混乱-弦理论的矩阵，我们研究涉及高激发弦的树级散射幅度。自从早期以来，尽管轻弦散射的幅度一直是弦理论的标志，但对激发弦的散射的研究却很少。关于黑洞混沌的最新结果，结合黑洞与弦之间的对应原理，表明振幅具有丰富的结构。我们回顾了通过反复地将光子散射离开初始的Tachyon（DDF形式主义）而形成受激弦的过程。在玻色子弦理论中，我们计算了一个任意的激励弦和任意数量的速度子的散射幅度。在高能量和高质量激发态下，这些振幅由积分点在球体（或上半平面）上的字符串顶点算符位置上的积分中的鞍点确定，因此可以得出“散射方程”的概括。我们找到了一个衰减为两个tachyons的激励弦的振幅的紧凑表达式，并研究了它对于一般激励弦的特性。我们发现，振幅是高度不稳定的，这是精确的激发弦状态和相对于其极化的超音速散射角的函数，这是混沌的迹象。