Radiative stability of tiny cosmological constant from the Swampland and quantized compactification

We address a quantization mechanism that can allow us to understand why the cosmological constant is not large under the quantum corrections from studying the circle compactification solution of the Standard Model coupled to Einstein gravity which is subject to the constraint of the Swampland conjectures. A novel result in the present work compared to the previous investigations in the literature is that the radius of the compactified dimension and the 4D cosmological constant $\Lambda_4$ must in fact be quantized. The quantization rule of the cosmological constant is given by $\Lambda_4\propto n^2$ with $n=1,2,3,4,\ldots$, which means that the values of $\Lambda_4$ are not arbitrary but only its specific values are allowed. In general, the quantum corrections as well as other effects would break this quantization rule. Hence, it could prevent the quantum fluctuations from generating zero-point energy contributions to the cosmological constant.