论文标题
紫外线相互作用标量场理论的确切FRG流的存在和构建
Existence and Construction of Exact FRG Flows of a UV-Interacting Scalar Field Theory
论文作者
论文摘要
我们证明了存在的存在并给出了欧几里得方程的欧几里得方程的欧几里得不变的精确解决方案，从而满足了紫外线限制中大规模和相互作用的真实标量$ ϕ^4 $理论的幼稚边界条件，以及在红外限制中的一般自由理论。该构建基于四点函数的自一致的ANSATZ，通过迭代方案产生动量依赖性相关功能。所得的相关器在所有调节器尺度上都界定，我们确定捕获紫外线和IR限制中渐近性的明确界限。此外，给定的构造原理可以扩展到其他系统，并且可能在研究精确溶液的一般特性方面有用。
We prove the existence and give a construction procedure of Euclidean-invariant exact solutions to the Wetterich equation in $d > 2$ dimensions satisfying the naive boundary condition of a massive and interacting real scalar $ϕ^4$ theory in the ultraviolet limit as well as a generalised free theory in the infrared limit. The construction produces the momentum-dependent correlation functions to all orders through an iterative scheme, based on a self-consistent ansatz for the four-point function. The resulting correlators are bounded at all regulator scales and we determine explicit bounds capturing the asymptotics in the UV and IR limits. Furthermore, the given construction principle may be extended to other systems and might become useful in the study of general properties of exact solutions.
