A theory of evolving natural constants embracing Einstein's theory of general relativity and Dirac's large number hypothesis

Taking a hint from Dirac's large number hypothesis, we note the existence of cosmic combined conservation laws that work to cosmologically long time. We thus modify or generalize Einstein's theory of general relativity with fixed gravitation constant $G$ to a theory for varying $G$, which can be applied to cosmology without inconsistency, where a tensor arising from the variation of G takes the place of the cosmological constant term. We then develop on this basis a systematic theory of evolving natural constants $m_{e},m_{p},e,\hslash ,k_{B}$ by finding out their cosmic combined counterparts involving factors of appropriate powers of $G$ that remain truly constant to cosmologically long time. As $G$ varies so little in recent centuries, so we take these natural constants to be constant.Comment: 29 pages, revtex

Detecting interactions between dark matter and photons at high energy e+e−e^+e^- colliders

We investigate the sensitivity to the effective operators describing interactions between dark matter particles and photons at future high energy $e^+e^-$ colliders via the \gamma+ \slashed{E} channel. Such operators could be useful to interpret the potential gamma-ray line signature observed by the Fermi-LAT. We find that these operators can be further tested at $e^+ e^-$ colliders by using either unpolarized or polarized beams. We also derive a general unitarity condition for $2 \to n$ processes and apply it to the dark matter production process $e^+e^-\to\chi\chi\gamma$.Comment: 13 pages, 8 figure

Entanglement entropy of (3+1)D topological orders with excitations

Excitations in (3+1)D topologically ordered phases have very rich structures. (3+1)D topological phases support both point-like and string-like excitations, and in particular the loop (closed string) excitations may admit knotted and linked structures. In this work, we ask the question how different types of topological excitations contribute to the entanglement entropy, or alternatively, can we use the entanglement entropy to detect the structure of excitations, and further obtain the information of the underlying topological orders? We are mainly interested in (3+1)D topological orders that can be realized in Dijkgraaf-Witten gauge theories, which are labeled by a finite group $G$ and its group 4-cocycle $\omega\in\mathcal{H}^4[G;U(1)]$ up to group automorphisms. We find that each topological excitation contributes a universal constant $\ln d_i$ to the entanglement entropy, where $d_i$ is the quantum dimension that depends on both the structure of the excitation and the data $(G,\,\omega)$. The entanglement entropy of the excitations of the linked/unlinked topology can capture different information of the DW theory $(G,\,\omega)$. In particular, the entanglement entropy introduced by Hopf-link loop excitations can distinguish certain group 4-cocycles $\omega$ from the others.Comment: 12 pages, 4 figures; v2: minor changes, published versio