论文标题
5维CHERN-SIMONS量规理论：从对称性通过边界条件进行对称性破裂的大规模自旋-2理论
5-Dimensional Chern-Simons Gauge Theory on an Interval: Massive Spin-2 Theory from Symmetry Breaking via Boundary Conditions
论文作者
论文摘要
在本说明中，我们通过压实额外的维度和几何对称性破裂来重新审视大量重力的4维理论。我们在尺寸上降低了（反）de Sitter组的5维拓扑Chern-Simons仪表理论。我们在端点上应用非平凡的边界条件以打破所有规格对称性。我们将量规连接的不同组成部分视为可逆的维尔贝因，并自旋连接将其解释为引力理论。在四个维度上的有效田间理论包括DRGT的潜在项，并具有在光谱中没有无质量重力的Kaluza-Klein状态。该理论的紫外线是5维重力$ l^{ - 1} $的普朗克量表。如果$ζ$是对称破坏的规模，而$ l $是间隔的长度，则最轻的Graviton $ m $和级别的$ n $（对于$ n <ll^{ - 1} $）kk gravitons $ m _ {\ rm kk}^{（n）} $是确定的$ m =（ζl^{ - 1}）^{\ frac {1} {2}}} \ ll m _ {\ rm kk}^{（n）} = nl^{ - 1} $。 4维planck质量为$ M _ {\ rm pl} \ sim（ll^{ - 3}）^{\ frac {1} {2}} $，我们找到了层次结构$ζ$ζ<m <m <l^{ - 1} <l^l^l^l^l^l^{ - 1} { - 1} <m pl}。
In this note, we revisit the 4-dimensional theory of massive gravity through compactification of an extra dimension and geometric symmetry breaking. We dimensionally reduce the 5-dimensional topological Chern-Simons gauge theory of (anti) de Sitter group on an interval. We apply non-trivial boundary conditions at the endpoints to break all of the gauge symmetries. We identify different components of the gauge connection as invertible vierbein and spin-connection to interpret it as a gravitational theory. The effective field theory in four dimensions includes the dRGT potential terms and has a tower of Kaluza-Klein states without massless graviton in the spectrum. The UV cut of the theory is the Planck scale of the 5-dimensional gravity $l^{-1}$. If $ζ$ is the scale of symmetry breaking and $L$ is the length of the interval, then the masses of the lightest graviton $m$ and the level $n$ (for $n<Ll^{-1}$) KK gravitons $m_{\rm KK}^{(n)}$ are determined as $m=(ζL^{-1})^{\frac{1}{2}}\ll m_{\rm KK}^{(n)}=nL^{-1}$. The 4-dimensional Planck mass is $m_{\rm Pl}\sim (Ll^{-3})^{\frac{1}{2}}$ and we find the hierarchy $ζ< m< L^{-1}<l^{-1}<m_{\rm Pl}$.
