论文标题
$ O（n）^3 $张量场理论中的共形对称和复合操作员
Conformal Symmetry and Composite Operators in the $O(N)^3$ Tensor Field Theory
论文作者
论文摘要
我们继续研究具有四分之一相互作用和远距离传播器的骨$ O（N）^3 $模型。对称组允许三个不同的不变$ ϕ^4 $复合算子，称为四面体，枕头和双轨。如Arxiv所示：1903.03578和Arxiv：1909.07767，四面体操作员在很大的限制中恰好是边缘的，并且纯粹是虚构的四面体耦合了一系列真实的红外固定点（由Tetrahedrahedradry coupl的绝对值）coupling two cout and cout and cout cout cout cout cout cout。这些固定点具有真正的关键指数和双线性操作员的真实范围，可满足单位性约束。这就提出了一个问题，尽管四面体耦合是虚构的，但总体上，该模型是否是统一的。在本文中，我们首先通过不同的正则化和重新归一化方案来重新逐渐重复上述结果。然后，我们讨论复合操作员的操作员混合，并通过调整来自远程ISING模型的类似证明，在红外固定点提供了模型在红外固定点的扰动证明。最后，我们在固定点确定缩放运算符，并计算$ ϕ^4 $和$ ϕ^2 $复合操作员的两点和三点功能。相关性具有预期的保形行为，并且OPE系数都是真实的，这加强了大型$ n $ cft是统一的说法。
We continue the study of the bosonic $O(N)^3$ model with quartic interactions and long-range propagator. The symmetry group allows for three distinct invariant $ϕ^4$ composite operators, known as tetrahedron, pillow and double-trace. As shown in arXiv:1903.03578 and arXiv:1909.07767, the tetrahedron operator is exactly marginal in the large-$N$ limit and for a purely imaginary tetrahedron coupling a line of real infrared fixed points (parametrized by the absolute value of the tetrahedron coupling) is found for the other two couplings. These fixed points have real critical exponents and a real spectrum of bilinear operators, satisfying unitarity constraints. This raises the question whether at large-$N$ the model is unitary, despite the tetrahedron coupling being imaginary. In this paper, we first rederive the above results by a different regularization and renormalization scheme. We then discuss the operator mixing for composite operators and we give a perturbative proof of conformal invariance of the model at the infrared fixed points by adapting a similar proof from the long-range Ising model. At last, we identify the scaling operators at the fixed point and compute the two- and three-point functions of $ϕ^4$ and $ϕ^2$ composite operators. The correlations have the expected conformal behavior and the OPE coefficients are all real, reinforcing the claim that the large-$N$ CFT is unitary.
