Research on Superstrings Compactified on Singular Manifolds via Conformal Field Theory

共形场论是研究弦理论各个方面的有用工具。另一方面，奇异流形上弦的研究是提取低能理论普适性质的关键。2002年，我们研究了超对称PP波背景下弦的某些性质。本文首先证明了在一般平面波背景下，由Penrose极限得到的光锥IIB Green-Schwarz作用量在费米子坐标下必然是二次的，并利用超协变导数写出了完全的二次作用量，然后考虑了S'和T2上最大超对称IIB平面波背景的紧化，证明了O（d，d; Z）（d=1，2）T-对偶，尽管在Hamilton中只出现了普通零模集的一半。首先，以偶四次势的厄米单矩阵模型为例，证明了相应规范理论的有效超势在跃迁点处是光滑的。我们还研究了四维N= 1U（N）规范理论中F项的引力修正，导出了全Tr R^R修正的一个紧致公式。我们还发现，它被再现为一个特殊的c=1 CFT相关器。

Conformal field theory has served as a useful tool for studying various aspects of string theory. On the other hand, the study of strings on singular manifolds is a key to extract a universal property of the low energy theories.In fiscal 2002, we studied some aspects of strings in supersymmetric PP wave backgrounds. First, we proved that the light-cone IIB Green-Schwarz action in general plane-wave backgrounds obtained as Penrose limits is necessarily quadratic in the fermionic coordinates, and wrote down the complete quadratic action using the supercovariant derivative.Next we considered the compactifications of the maximally supersymmetric IIB plane-wave background on S' and T2 and showed that the O(d, d; Z) (d=1, 2) T-duality, despite that only half of the ordinary set of zero modes appeared in the HamiltonianIn fiscal 2003, we mainly worked on the Dijkgraaf-Vafa theory. First, considering a hermitian one-matrix model with an even quartic potential as an example, we showed that the value of the effective superpotential of the corresponding gauge theory was smooth at the transition point. We also studied the gravitational corrections to the F-term in four-dimensional N=1 U(N) gauge theories with flavors, and derived a compact formula for the the full Tr R^R correction. We also found that it was reproduced as a special c=1 CFT correlator.