弦論的高能散射

Abstract

弦論的高能散射至少有三大特性與場論極為不同，這些特性使弦論能有自恰的量子引 力。第一特性是弦論的高能散射振幅為軟指數退化，此與場論的硬冪次退化不同。第二 特性是弦的振幅俱有無限多個Regge 共振態。第三是弦散射振幅的高能線性關係或高能 對稱，此無限對稱是自恰量子引力的基礎。為了進一步了解上述三個特性及其相互之間 的關係，我們將研究以下: 1. 計算弦與D-branes, O-planes 及orbifold 等背景下的高能散射振幅，並從中比較其上 述三大特性的關係。 2. 有一些彎曲空間的弦背景其粒子譜是可以精解的，我們將試著建構vertex 算符並計 算其高能相干函數。 3. 弦的高溫性質與高能性質有些相似處，我們將研究弦的熱力學，特別是其在緊緻空 間時的行為。

There are three fundamental characteristics of high energy string scatterings. The first is the softer exponential fall-off behavior of the form factors of high-energy string scatterings in contrast to the power-law (hard) behavior of point-particle field theory scatterings. The second is the existence of infinite Regge poles in the form factor of string scattering amplitudes. The last one is the existence of infinite linear relations among string scattering amplitudes of different string states for each fixed mass level. To understand the above three fundamental properties of string scatterings and the relationships among them, we would like to study the followings: 1. One of the main purpose of this project is to calculate high energy string scatterings in various string systems, e.g. scatterings from D-branes, O-planes and orbifold backgrounds etc. We can then study and compare the above three characteristics in these scattering amplitudes. 2. There are several solvable curved string backgrounds, which one can exactly calculate the spectrum. We will try to calculate high energy correlation functions of these backgrounds. 3. A closely related subject of high energy string is the high temperature behavior of string theory, or string thermodynamics. One interesting topic is string gas in compact space. We will try to understand its relation to high energy string scattering in compact space of our previous works.