（超）弦論中所有零點之研究

Abstract

本文透過弦論的曲線積分表示式來探討其振幅的零點結構。首先我們指出，在玻色弦理論中，迅子振幅的曲線積分表示式與動量位移後的Tr(ϕ^3)振幅完全一致。將曲線進行骨架建構法（scaffold）操作，可對應到在世界面上進行算子積展開（OPE）極限，進而得到高激發態的振幅。在此圖像下，我們證明n點、階數N的弦論振幅會同時具有兩種零點結構：一為與n點迅子振幅相同的零點；二為在骨架建構法（scaffold）操作過程中引入的y變數所對應的零點，而這些額外的零點可追溯至其骨架建構 （scaffold）前的(2^N)n 點迅子振幅中。 此外，應用相同方法於超弦中的超迅子振幅，可揭示開弦超弦理論中的新型零點，這些可視為超對稱性的展現。最後，我們分析四點與六點的超膠子振幅，成功識別其零點結構，並由骨架建構法（scaffold）操作重建出超楊–米爾斯理論。我們亦探討彩色費米子振幅的場論極限，並從曲線積分形式還原其結構。

In this paper, we study the zeros of string theory utilizing its curve-integral representation. Firstly, we note that for bosonic strings the tachyon amplitude in curve-integral representation is identical to the kinematic shifted Tr( ϕ ^3) amplitude. Scaffolding is then equivalent to taking the OPE limit of vertex operators on the string world-sheet, which yields amplitude of higher excitations. Using this picture, we derive that the n-point level-N scattering amplitude shares the same set of zeros as the n-point tachyon amplitude, along with additional zeros associated with the scaffolding y-variables, which are inherited from its pre-scaffold image, namely the (2^N)n-point tachyon amplitude. Doing the same for the super-tachyon amplitude, exposes new zeros for the open superstring, which can be viewed as the avatar of supersymmetry. Finally we also consider the gluino amplitude at four and six points, identifying its zero and recovering super Yang-Mills via scaffolding. Finally we consider the field theory limit of colored fermion amplitudes from the curve-integral form.