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

在SU(N)晶格规范理论的大N极限中，存在时空自由度被吸收到SU(N)内部自由度中的可能性。本文研究了具有扭曲边界条件的1到4格上的时空约简模型。1)采用时空简化模型对弦张力进行了精确计算。在常用的SU(N)晶格规范理论中也计算了弦张力，并将结果外推到大N，外推值与时空约简模型直接得到的值完全吻合，从而证明了约简模型的正确性。2)具有两个伴随费米子的时空约简模型具有受红外不动点支配的共形理论的特征。我也证明了，有一个伴随费米子的理论具有支持这个理论是一个约束理论的性质。

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.