arXiv 0901.04592009-01-05hep-thhep-ph

非对易场论中IR/UV的引力消去

Elimination of IR/UV via Gravity in Noncommutative Field Theory

N. Kersting, J. Yan

备注：: 6 pages; MPLA version
DOI：: 10.1142/S0217732308026571

摘要：

具有非对易几何的粒子物理模型通常会受到红外和紫外自由度的明显非威尔逊耦合的影响，称为“IR/UV问题”，这往往会损害它们的唯象相关性。在这封信中，我们明确地展示了如何通过将NCG与引力耦合来纠正这一点。在最简单的情况下，拉格朗日乘上一个非常数的背景度量;在$ϕ-4$理论中，$\int d^4 x ϕ\star ϕ= \int d^4 x ϕ^2$不再成立的定理，场传播子被一个因子修改，该因子取决于NCG和度量的变化。当传播动量逐渐变大时，该因子的适当限制将根除IR/UV问题。由于引力和NCG相互耦合，人们可能会期望在度规中出现反对称分量。宇宙学的影响，这种随后进行了讨论。

英文摘要：

Models of particle physics with Noncommutative Geometry (NCG) generally suffer from a manifestly non-Wilsonian coupling of infrared and ultraviolet degrees of freedom known as the "IR/UV Problem" which would tend to compromise their phenomenological relevance. In this Letter we explicitly show how one may remedy this by coupling NCG to gravity. In the simplest scenario the Lagrangian gets multiplied by a nonconstant background metric; in $ϕ-4$ theory the theorem that $\int d^4 x ϕ\star ϕ= \int d^4 x ϕ^2$ is no longer true and the field propagator gets modified by a factor which depends on both NCG and the variation of the metric. A suitable limit of this factor as the propagating momentum gets asymptotically large then eradicates the IR/UV problem. With gravity and NCG coupled to each other, one might expect anti-symmetric components to arise in the metric. Cosmological implications of such are subsequently discussed.

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