突破多味规理论质量异常维数上限：自举法揭示SU(12)约束

79 浏览量更新于2024-07-16 收藏 616KB PDF 举报

本文主要探讨了在多味规范理论中质量异常维度的上限问题，利用了数值共形引导程序这一工具来研究具有全局对称性的三维共形场理论。作者们特别关注的是与自旋0运算符四点函数相关的交叉关系，这些函数属于SU(N)对称性的伴随表示。具体案例中，当自旋0运算符φ̄_k_i的缩放维度小于1.71时，理论被认为可能包含一个自旋0的SU(N)破坏相关的操作符。这对于12种风味的量子色动力学（QCD）模型的晶格模拟具有重要意义，因为这类破坏性操作符可能会由交错费米子的味破坏效应引起，导致理论的红外行为偏离预期。在基于交错费米子的12风味QCD的模拟实验中，尚未观察到这种破坏现象的迹象。因此，如果假设不存在上述相关操作符，作者们通过共形对称约束得出一个质量异常维度的上限。这个上限虽然不非常严格，但在数值精度上是确定的。值得注意的是，文章还揭示了一个类似的特性，即在边界曲线中，另一个破坏操作符的缩放尺度表现出类似扭结的行为。这项研究采用的是共形bootstrap方法，这是一种在高维量子场论中的强大工具，它通过非perturbative的分析来约束理论空间中的参数，从而给出物理量如维度的精确估计。通过这种方法，作者们不仅验证了理论预测的有效性，也为理解多味规范理论中的潜在新现象提供了重要的见解。这篇文章不仅贡献了一个关于质量异常维度上限的具体数值结果，还展示了共形bootstrap技术在探索复杂量子场论性质中的应用前景。这对于理论物理学家来说，是一个关于规范理论和共形对称性的重要进展，对于实际的QCD模型研究也有着潜在的实际意义。

PTEP 2016, 053B03 H. Iha et al.

S(1.2). Then, the mass anomalous dimension γ

∗

and the scaling dimension 

(at the ﬁxed point)

are related by

∗

= 3 − 

. (1.5)

This also directly follows from the partially conserved axial current (PCAC) relation.

In Sect. 2, we consider a four-point function of a spin 0 adjoint operator φ

without specifying its

actual microscopic structure such as Eq. (1.4).

We derive the crossing relation associated with the

four-point function,

basically following the notational conventions of Ref. [18]. Then, in Sect. 3,

we apply the numerical conformal bootstrap to the crossing relation. For this, we used a semideﬁnite

programming code, the SDPB of Ref. [35].

In this way, among other things, we found that for N = 12 the system contains a spin 0 relevant

operator in the representation [N − 1, N − 1, 1, 1] of SU(N),

when



< 1.71, for N = 12. (1.6)

Since this relevant operator in the [N − 1, N − 1, 1, 1] representation appears in the operator product

expansion (OPE) of two φ

s, if the latter is identiﬁed with the pseudo-scalar density in Eq. (1.4),

this is a scalar density. Such an SU(12) non-invariant operator is not radiatively induced, even if

it is relevant, if our regularization preserves the SU(12) symmetry. We note, however, that in all

existing lattice simulations of the 12-ﬂavor QCD, the staggered fermion [49]isemployedtoprevent

the fermion mass operator (which is believed to be a unique spin 0 SU(12)-invariant relevant operator

associated with the infrared ﬁxed point under consideration) from being radiatively induced. This is

accomplished by the exact U (1)

symmetry [50] that the massless staggered fermion possesses. Still,

however, the staggered fermion cannot preserve the full SU(12) ﬂavor symmetry (the so-called taste

breaking). Generally, when the regularization does not preserve a symmetr y, relevant operators that

are not invariant under the symmetry are radiatively induced and, to achieve the desired continuum or

low-energy limit, one has to tune the coefﬁcients of those non-invariant operators in the action. The

fact that actual lattice simulations [12,39–47]ofthe12-ﬂavor QCD are consistent with the existence

of an infrared ﬁxed point without such a ﬁne-tuning strongly indicates that the theory does not contain

the above SU(12) non-invariant relevant operator in the spectrum.

Thus, assuming the absence of the spin 0 relevant operator in the representation [N − 1,

N − 1, 1, 1], we have the inequality 

≥ 1.71. Then the upper bound on the mass anomalous

dimension (1.1) follows from the relation (1.5).

We stress that our upper bound (1.1) is a physical proper ty of a conformal ﬁeld theory at the infrared

ﬁxed point under consideration. The validity of our upper bound and whether one uses the staggered

fermion in actual lattice simulations are completely independent issues. We have used the fact indi-

cated by existing lattice simulations, just to support our assumption on the absence of the spin 0

relevant operator in the representation [N − 1, N − 1, 1, 1] around the ﬁxed point. Whether there

We do not assume the underlying gauge theory either; we assume only that the theory is conformal and

possesses a global SU(N) symmetry.

We learned that this crossing relation had already been derived in Ref. [25]. We would like to thank the

referee for pointing out this fact.

We label representations of SU(N ) by a list of the (non-increasing) number of boxes in each column of the

corresponding Young tableau. For example, the adjoint representation is denoted as [N − 1, 1].ForN = 12,

we should say [11, 11, 1, 1] rather than [N − 1, N − 1, 1, 1], but in this paper we use the latter notation even

for N = 12. This remark applies also for other representations and for other values of N .

3/15

剩余14页未读，继续阅读

weixin_38674763

粉丝: 6
资源: 967

突破多味规理论质量异常维数上限：自举法揭示SU(12)约束

论文研究 - 移动服务市场中服务质量维度的比较：来自新兴市场的证据

保形几何和（超）保形高自转规理论

维度统计：2019年年度报告.PDF

数据仓库中 数据质量、维度模型与数据安全

提高matlab生成矩阵的维度上限

怎么用reshape（）改变他们的维度举个例子

PSO算法维度不匹配

如果交叉报表需要多行行维度呢？

大数据管理平台中数据存储中 数据仓库中数据质量、维度模型与数据安全的

请提供一段代码：使用 numpy 库中的 ndim 函数来判断自己的数据的维度

最新资源

数据仓库中数据质量、维度模型与数据安全

大数据管理平台中数据存储中数据仓库中数据质量、维度模型与数据安全的