论文标题
随机张量模型重新归一化组流量的局部截断的可靠性
Reliability of the local truncations for the random tensor models renormalization group flow
论文作者
论文摘要
张量模型的重新归一化组的标准非扰动方法通常集中在纯粹的局部电位近似上（即仅涉及其概括性痕迹和它们的产物），并显示出强烈违反修改后的病房身份。本文作为我们最近的贡献的延续[物理评论D 101，106015（2020）]，旨在调查具有病房身份的近似计划兼容，并在$ n $ n $ limit中可观察到的2n $ points介于$ 2N $ - 点之间。我们分别考虑两个不同的近似值：在第一个近似值中，我们尝试从litim调节器的轻微修改中构建局部电位近似，以使其在通常的意义上保持最佳状态，并在深紫外线和深ir限制中保留边界条件。在第二个中，我们在截断中介绍了衍生耦合，并表明与病房身份的兼容性意味着$β$ - 功能之间的牢固关系，允许在非支流部门中关闭无限流程的无限流程层次结构，在衍生物扩张中最多可以给定顺序。最后，使用相关性函数在大$ n $ limit中的确切关系，我们表明，严格的局部截断不足以达到关键指数的确切值，从而强调了这些可观察到的牢固关系所起的作用，考虑到流动的行为。以及在两种不同的近似方案中讨论的多条算子的作用。在这两种情况下，我们都将结论与文献中获得的结果进行了比较，并得出结论，在给定的顺序下，考虑到以系统的方式观察到的可观察到的可观测值之类的确切功能关系，我们可以强烈改善精确RG方程的近似值的物理相关性。
The standard nonperturbative approaches of renormalization group for tensor models are generally focused on a purely local potential approximation (i.e. involving only generalized traces and product of them) and are showed to strongly violate the modified Ward identities. This paper as a continuation of our recent contribution [Physical Review D 101, 106015 (2020)], intended to investigate the approximation schemes compatibles with Ward identities and constraints between $2n$-points observables in the large $N$-limit. We consider separately two different approximations: In the first one, we try to construct a local potential approximation from a slight modification of the Litim regulator, so that it remains optimal in the usual sense, and preserves the boundary conditions in deep UV and deep IR limits. In the second one, we introduce derivative couplings in the truncations and show that the compatibility with Ward identities implies strong relations between $β$-functions, allowing to close the infinite hierarchy of flow equations in the non-branching sector, up to a given order in the derivative expansion. Finally, using exact relation between correlations functions in large $N$-limit, we show that strictly local truncations are insufficient to reach the exact value for the critical exponent, highlighting the role played by these strong relations between observables taking into account the behavior of the flow; and the role played by the multi-trace operators, discussed in the two different approximation schemes. In both cases, we compare our conclusions to the results obtained in the literature and conclude that, at a given order, taking into account the exact functional relations between observables like Ward identities in a systematic way we can strongly improve the physical relevance of the approximation for exact RG equation.
