Lavaei Leila
Department of Physics, Qom University of Technology, Qom, Iran.
Sci Rep. 2024 Aug 12;14(1):18685. doi: 10.1038/s41598-024-69554-6.
Some important problems in science do not have analytical solutions in four dimensions including QCD, but they are integrable in two dimensions. For many years, scientists have been trying to find a relation between two-dimensional and four-dimensional space-time to explain the real problem in four dimensions by accurately solving the appropriate model in two dimensions. In this paper, an interesting relation between (generalized two-dimensional Yang-Mills) and Maxwell construction has been found, which can be a starting point for finding more relations between two-dimensional and four-dimensional space-time, so this paper can play an important role in the advancement of science. For this purpose, first, the large-N behavior of the quartic-cubic generalized two-dimensional Yang-Mills U(N) on a sphere is investigated for finite cubic couplings. It is shown that there are two phase transitions one of which is of third order, which is similar to previous papers, and the other one is of second order, which is a novel result. Second, (for ) and Maxwell construction are compared with each other and a relationship between two-dimensional space-time, which is integrable, and four-dimensional space-time is obtained.
科学中的一些重要问题在包括量子色动力学（QCD）在内的四维空间中没有解析解，但它们在二维空间中是可积的。多年来，科学家们一直试图找到二维和四维时空之间的关系，以便通过精确求解二维空间中的适当模型来解释四维空间中的实际问题。本文发现了（广义二维杨 - 米尔斯理论）与麦克斯韦构造之间的一种有趣关系，这可能是找到二维和四维时空之间更多关系的一个起点，因此本文在科学进步中可以发挥重要作用。为此，首先，研究了球面上有限立方耦合下四次 - 三次广义二维杨 - 米尔斯U(N)的大N行为。结果表明存在两个相变，其中一个是三阶相变，这与之前的论文类似，另一个是二阶相变，这是一个新结果。其次，将（对于 ）与麦克斯韦构造进行了比较，并得到了可积的二维时空与四维时空之间的关系。
