论文标题
来自Kaluza-Klein紧凑型和度量重塑的允许复杂标量
Allowable Complex Scalars from Kaluza-Klein Compactifications and Metric Rescalings
论文作者
论文摘要
最近，关于量子重力应允许哪些复杂指标的讨论。这些讨论认为物质领域是真正的价值。我们的观察是，对于紧缩的解决方案，需要在高维父理论中需要该理论路径积分的融合是有意义的。紧凑时，这允许在低维理论中进行更一般的物质配置，特别是它允许复杂的标量字段，并在其虚构部分上绑定。在较高的曲率校正存在下，类似的考虑适用于度量重新列车。我们以无限建议的示例来说明这种效果，其中通常需要标量字段才能采用复杂的值。我们发现，如果电势足够平坦，则存在复杂的无边界溶液并满足派生的结合。例如，对于$ d $尺寸的紧凑型，内部音量模量的限制为$ \ textrm {im} \，（ϕ）$，nosition卷模量读取$ v _ {，ϕ}/ϕ}/v <\ sqrt {\ sqrt {\ frac {\ frac {d-4} {d-4} {d-2-2} {d-2} {d-2} {d-2}} {d-2}}/3 \ s $ Swampland猜想。
Recently there have been discussions about which complex metrics should be allowable in quantum gravity. These discussions assumed that the matter fields were real valued. We make the observation that for compactified solutions it makes sense to demand convergence of the theory's path integral in the higher-dimensional parent theory. Upon compactification this allows for more general matter configurations in the lower-dimensional theory, in particular it allows for complex scalar fields, with a bound on their imaginary parts. Similar considerations apply to metric rescalings in the presence of higher curvature corrections. We illustrate this effect with the example of the no--boundary proposal, in which scalar fields are typically required to take complex values. We find that complex no-boundary solutions exist, and satisfy the derived bound, if the potential is sufficiently flat. For instance, for a compactification from $D$ dimensions, the bound on the imaginary part $\textrm{Im}\,(ϕ)$ of the internal volume modulus reads $V_{,ϕ}/V < \sqrt{\frac{D-4}{D-2}}/3\sqrt{2}.$ This leads to a mild tension with swampland conjectures.
