A Renormalizable 4-Dimensional Tensor Field Theory
A Renormalizable 4-Dimensional Tensor Field Theory
复制标题
可重整的4维张量场论
DOI：
10.1007/s00220-012-1549-1
复制
发表时间：
2011
影响因子：
2.4
通讯作者：
V. Rivasseau
中科院分区：
文献类型：
--
作者：
J. B. Geloun;V. Rivasseau
在摄动理论中，我们证明了在U(1)4上补充常用玻色子的古劳彩色张量模型的积分版本是可重整到所有阶的。该模型是四维欧几里得引力中时空量化所期望的类型，是这种可重整模型的第一个例子。它的顶点和传播子和四维群场论一样是四股的，但是没有对股进行规范平均。也许令人惊讶的是，该模型是$${\phi^6}$$型而不是$${\phi^4}$$型，因为两种不同的$${\phi^6}$$型相互作用是对数发散的，即在重整化群意义上是边缘的。重整化证明依赖于多尺度分析。它通过幂计数定理来识别所有发散图。这些发散图有一种特殊的内部和外部结构，叫做曲线图。单调图在彩色张量模型的1/N展开中占主导地位，并推广了矩阵模型的平面带状图。为这类图建立了一个新的局部性原理，它允许通过裸拉格朗日相互作用形式的反项来重新规范化它们的散度。该模型还有一个意想不到的反常对数发散$${(\int \phi^2)^2}$$项，可以解释为纯重力产生标量物质场。
We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on U(1)4 is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of space-time in 4D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are four-stranded like in 4D group field theories, but without gauge averaging on the strands. Surprisingly perhaps, the model is of the $${\phi^6}$$ rather than of the $${\phi^4}$$ type, since two different $${\phi^6}$$-type interactions are log-divergent, i.e. marginal in the renormalization group sense. The renormalization proof relies on a multiscale analysis. It identifies all divergent graphs through a power counting theorem. These divergent graphs have internal and external structure of a particular kind called melonic. Melonic graphs dominate the 1/N expansion of colored tensor models and generalize the planar ribbon graphs of matrix models. A new locality principle is established for this category of graphs which allows to renormalize their divergences through counterterms of the form of the bare Lagrangian interactions. The model also has an unexpected anomalous log-divergent $${(\int \phi^2)^2}$$ term, which can be interpreted as the generation of a scalar matter field out of pure gravity.