Research on Superstrings Compactified on Singular Manifolds via Conformal Field Theory

共形场理论已成为研究弦理论各个方面的有用工具。另一方面，对奇异流形上弦的研究是提取低能量理论普适性的关键。在2002财政年度，我们研究了超对称PP波背景下弦的某些方面。首先，我们证明了一般平面波背景下的光锥IIB格林-施瓦兹作用量在费米子坐标下必然是二次的，并且利用超协变导数写下了完全的二次作用量；其次，我们考虑了极大超对称IIB平面波背景在S‘和T2上的紧致，证明了O(d，d；Z)(d=1，2)T-对偶性，尽管通常的零模集合只有一半出现在哈密顿中。首先，以具有偶数四次势的厄米特单阵模型为例，证明了相应规范理论的有效超势在过渡点是光滑的。我们还研究了四维N=1U(N)规范理论中F项的引力修正，得到了完整的Tr R^R修正的紧凑公式。我们还发现，它被复制为一个特殊的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.