论文标题
从Hagedorn到Lee-Yang：$ \ Mathcal {n} = 4 $ SYM理论的分区功能有限$ n $
From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
论文作者
论文摘要
我们研究了r x s^3上的量规u（n）的最大超对称性阳米尔斯理论的热力学，对ADS_5 x s^5的IIB级超弦理论的双重动力学。尽管这两种理论都是在无限N处表现出Hagedorn行为的众所周知的，但我们发现证据表明，这是由大但有限的n：分区功能的零元素在复杂温度平面中凝结成两个弧的零元素的替代，这些弧在固定的温度平面上捏成两个弧线，这些弧线在限制限制过渡的温度下将真实的轴捏住。具体而言，我们通过对包含两个复杂标量的SU（2）扇区（2）扇区的N <= 7的（未精制和精制）分区函数的精确计算，以及含有3个复杂标量和2个费米子的SU（2 | 3）扇区的n <= 5。为了获得这些明确的结果，我们利用分区函数与数学家所知的等效性作为任意场含量的莫莱恩 - 韦尔公式来进行任意野外含量。通过此molien-weyl公式，我们还为较大部门产生了精确的结果。
We study the thermodynamics of the maximally supersymmetric Yang-Mills theory with gauge group U(N) on R x S^3, dual to type IIB superstring theory on AdS_5 x S^5. While both theories are well-known to exhibit Hagedorn behavior at infinite N, we find evidence that this is replaced by Lee-Yang behavior at large but finite N: the zeros of the partition function condense into two arcs in the complex temperature plane that pinch the real axis at the temperature of the confinement-deconfinement transition. Concretely, we demonstrate this for the free theory via exact calculations of the (unrefined and refined) partition functions at N<=7 for the su(2) sector containing two complex scalars, as well as at N<=5 for the su(2|3) sector containing 3 complex scalars and 2 fermions. In order to obtain these explicit results, we use a Molien-Weyl formula for arbitrary field content, utilizing the equivalence of the partition function with what is known to mathematicians as the Poincare series of trace algebras of generic matrices. Via this Molien-Weyl formula, we also generate exact results for larger sectors.
