Properties of infinite product amplitudes: Veneziano, Virasoro, and Coon

Veneziano Variations: How Unique are String Amplitudes?

String theory offers an elegant and concrete realization of how to consistently couple states of arbitrarily high spin. But how unique is this construction? In this paper we derive a novel, multi-parameter family of four-point scattering amplitudes exhibiting i) polynomially bounded high-energy behavior and ii) exchange of an infinite tower of high-spin modes, albeit with a finite number of states at each resonance. These amplitudes take an infinite-product form and, depending on parameters, exhibit mass spectra that are either unbounded or bounded, thus corresponding to generalizations of the…

广义 Veneziano 振幅与 Virasoro 振幅

Generalized Veneziano and Virasoro amplitudes

本文通过超定非线性递推关系刻画广义 Veneziano 与 Virasoro 振幅，解析得到广义 Veneziano 的双参数族，并证明广义 Virasoro 的唯一自洽谱为弦谱。

On the unitarity and low energy expansion of the Coon amplitude

The Coon amplitude is a deformation of the Veneziano amplitude with logarithmic Regge trajectories and an accumulation point in the spectrum, which interpolates between string theory and field theory. With string theory, it is the only other solution to duality constraints explicitly known and it constitutes an important data point in the modern S-matrix bootstrap. Yet, its basics properties are essentially unknown. In this paper we fill this gap and derive the conditions of positivity and the low energy expansion of the amplitude. On the positivity side, we discover that the amplitude switche…

任意激发态弦的Veneziano与Shapiro-Virasoro振幅

Veneziano and Shapiro-Virasoro amplitudes of arbitrarily excited strings

本文基于相干弦态形式体系，将Veneziano和Shapiro-Virasoro振幅推广至玻色弦理论中的任意激发态，并推导了三弦相互作用的协变形式及连接开闭弦散射的广义Kawai-Lewellen-Tye关系。

Accumulation-Point Amplitudes in String Theory

We point out some common qualitative features of the Coon amplitude$\unicode{x2014}$a family of deformations of the Veneziano amplitude with logarithmic Regge trajectories$\unicode{x2014}$and the open string scattering amplitude for strings ending on a D-brane in AdS. Both reduce to the Veneziano amplitude at relatively low energies. Both systems have an accumulation point in their spectrum, with an infinite number of states below a certain energy. The approach to this point is very similar. Both have the same high-energy fixed-angle behavior. Nevertheless, we find some differences in the spec…

任意维度下的 Veneziano 振幅与一个 Virasoro-Shapiro 分振幅

The Veneziano Amplitude in any Dimension and a Virasoro-Shapiro Partial Amplitude

本文将 Veneziano 分振幅推广至任意维度世界面，并在 d=2 时由共形交比分解 Virasoro-Shapiro 振幅，同时提出残差自旋交替的自举原理以寻找无快子超对称形式。