Research On Supersymmetric Gauge Theories Via Matrix Models : A New Approach

1.利用Dijkgraaf-Vafa理论研究了四维N= 1U（N）味规范理论中F项的引力修正。我们导出了一个简洁的矩阵模型曲线上的素形式的环贡献公式，并发现完整的TrR^R修正被再现为单个c=1 CFT湍流器的一个特殊动量扇区。2.我们证明了酉1矩阵模型与耦合到2N个适当势的厄米1矩阵模型在1/N展开中的所有阶完全等价。这种二重性是有用的，例如：（1）明确地证实了N=2纯SU（2）规范理论的酉矩阵表述正确地再现了亏格1拓扑弦振幅;（2）在酉矩阵模型和Chern-Simons矩阵模型中特殊几何关系的推导; Moody代数G2 H及其与D=5，N=2纯超引力的联系在D=5的纯超引力下，玻色运动方程和比安奇恒等式与G2 H σ模型的3阶截断方程在更高的阶项上是一致的。4.我们得到了在平坦空间和pp波背景下弦的无穷多个守恒非定域荷。5.我们证明了低维纯旋量超弦与双旋量超弦是上同调等价的。6.我们研究了D=6纯超杨-米尔斯理论的零维约化模型，证明了大N极限描述了（2，0）小弦理论.此外，我们还确定了IIB矩阵模型中一些未知的顶点算符，并证实它们与D-瞬子背景中四点引力子振幅的运动学因子是一致的。

1.We studied the gravitational corrections to the F-term in four-dimensional N=1 U(N) gauge theories with flavors, using the Dijkgraaf-Vafa theory. We derived a compact formula for the annulus contribution in terms of the prime form on the matrix model curve, and found that the full TrR^R correction was reproduced as a special momentum sector of a single c=1 CFT correlator.2.We have shown that Unitary 1-matrix models are exactly equivalent to hermitian 1-matrix models coupled to 2N vectors with appropriate potentials, to all orders in the 1/N expansion. This duality is useful, for example, for : (1) an explicit confirmation that the unitary matrix formulation of the N=2 pure SU(2) gauge theory correctly reproduces the genus-1 topological string amplitude (2) derivations of the special geometry relations in unitary as well as the Chern-Simons matrix models.3.We studied a one-dimensional sigma model associated with the hyperbolic Kac-Moody algebra G2H and its link to D=5, N=2 pure supergravity. The bosonic equations of motion and the Bianchi identity for D=5 pure supergravity match the equations of the level 3 truncation of the G2H sigma model up to higher level terms.4.We have obtained sets of infinite number of conserved nonlocal charges of strings in a flat space and pp-wave backgrounds.5.We showed that the lower-dimensional pure-spinor superstrings were cohomologically equivalent to the double-spinor superstrings in the same dimensions, and that the former were closely related to noncritical strings.6.We studied the zero-dimensional reduced model of D=6 pure super Yang-Mills theory and argued that the large N limit described the (2,0) Little String Theory. Also, we determined some so-far unknown vertex operators for the IIB matrix model and confirmed that they were consistent with the kinematical factor of a four-point graviton amplitude in a D-instanton background.