In)validity of large N orientifold equivalence
In)validity of large N orientifold equivalence
复制标题
In) 大 N 方向等效的有效性
DOI：
10.1103/physrevd.74.105019
复制
发表时间：
2006
影响因子：
5
通讯作者：
L. Yaffe
中科院分区：
文献类型：
--
作者：
M. Unsal;L. Yaffe
有人认为，超对称 SU(N) Yang-Mills 理论的玻色子扇区，以及反对称（或对称）张量表示中具有单个费米子的 QCD，在 N{yields}{infinity} 极限上是等效的。如果属实，这种对应关系可以为了解真实 QCD（具有基本表示费米子）的性质提供有用的见解，例如对非微扰真空能量、手性凝聚和各种其他可观察量的预测[经过 O(1/N) 校正]。已经出现了几篇声称已经证明了这个大的 N 'orientifold 等价性' 的论文。通过考虑 R{sup 3}xS{sup 1} 上的压缩理论，我们明确地表明，由于 QCD 中带有反对称（或对称）张量表示费米子的电荷共轭对称性的自发对称性破缺，这种大的 N 等价性在足够小的半径下失败，我们的分析是可靠的。与超杨-米尔斯理论不同，该理论对于小半径也是手性对称的。这种情况完全类似于基于轨道投影的大 N 等价：简单的对称实现条件对于大 N 等价的有效性既是必要的也是充分的。是否满足这些对称性实现条件取决于所考虑的理论的特定非微扰动力学。完整的电荷共轭对称性对于大 N 方向等效性的有效性是必要的。目前尚不清楚 R{sup 4}（或 R{sup 3}xS{sup 1} 足够大的半径）上是否满足此条件。« less
It has been argued that the bosonic sectors of supersymmetric SU(N) Yang-Mills theory, and of QCD with a single fermion in the antisymmetric (or symmetric) tensor representation, are equivalent in the N{yields}{infinity} limit. If true, this correspondence can provide useful insight into properties of real QCD (with fundamental representation fermions), such as predictions [with O(1/N) corrections] for the nonperturbative vacuum energy, the chiral condensate, and a variety of other observables. Several papers asserting to have proven this large N 'orientifold equivalence' have appeared. By considering theories compactified on R{sup 3}xS{sup 1}, we show explicitly that this large N equivalence fails for sufficiently small radius, where our analysis is reliable, due to spontaneous symmetry breaking of charge-conjugation symmetry in QCD with an antisymmetric (or symmetric) tensor representation fermion. This theory is also chirally symmetric for small radius, unlike super-Yang-Mills theory. The situation is completely analogous to large-N equivalences based on orbifold projections: simple symmetry realization conditions are both necessary and sufficient for the validity of the large N equivalence. Whether these symmetry realization conditions are satisfied depends on the specific nonperturbative dynamics of the theory under consideration. Unbroken charge-conjugation symmetry is necessary for validity of the large N orientifold equivalence. Whethermore » or not this condition is satisfied on R{sup 4} (or R{sup 3}xS{sup 1} for sufficiently large radius) is not currently known.« less