Study of twisted space-time reduced model in the large N limit

在SU（N）格点规范理论的大N极限下，时空自由度有可能被SU（N）内部自由度吸收。 本文主要研究了在扭曲边界条件下的四分之一格点上的时空约化模型。1）利用时空约化模型对弦张力进行了精确计算。 在通常的SU（N）格点规范理论中也计算了弦张力，并将结果外推到大N。外推值与由时空约化模型直接得到的值完全一致，从而证明了约化模型的正确性。2）具有两个伴随费米子的时空约化模型具有红外不动点支配的共形理论的特性。 我还表明，理论有一个单一的伴随费米子的属性，支持这一理论是一个封闭的理论。

In the large N limit of the SU(N) lattice gauge theory, there is a possibility that the space-time degrees of freedom are absorbed into the SU(N) internal degrees of freedom. In this work, I study the space-time reduced model defined on a one to the forth lattice with twisted boundary condition.1) The precise calculation of the string tension is made using the space-time reduced model. String tension is also calculated in the usual SU(N) lattice gauge theory and results are extrapolated to large N. The extrapolated value perfectly coincides with that obtained directly by space-time reduced model, thus demonstrating the correctness of the reduced model.2) The space-time reduced model having two adjoint fermions is shown to have properties which are characteristic to the conformal theory governed by an infrared fixed point. I also show that the theory having a single adjoint fermion has the properties which support that this theory is a confining theory.