Research on Superstrings Compactified on Singular Manifolds via Conformal Field Theory

共形场论已经成为研究弦理论各个方面的有用工具。另一方面，研究奇异流形上的弦是提取低能理论的普遍性质的关键。在2002财年，我们研究了超对称PP波背景下弦的一些方面。首先，我们证明了在一般平面波背景下以Penrose极限得到的光锥IIB Green-Schwarz作用在费米子坐标系下必然是二次的，并利用超协变导数写出了完全的二次作用。接下来，我们考虑了S'和T2上最大超对称IIB平面波背景的紧化，并证明了O(d, d； Z) (d= 1,2) t二象性，尽管只有一半的普通零模态出现在哈密顿模型中。2003财政，我们主要研究Dijkgraaf-Vafa理论。首先，以具有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值在过渡点处是光滑的。我们还研究了四维N=1 U(N)规范理论中f项的引力修正，并推导了完整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.