Topological Strings and Quantum Spectral Problems

We consider certain quantum spectral problems appearing in the study of local Calabi-Yau geometries. The quantum spectrum can be computed by the Bohr-Sommerfeld quantization condition for a period integral. For the case of small Planck constant, the periods are computed perturbatively by deformation of the Omega background parameters in the Nekrasov-Shatashvili limit. We compare the calculations with the results from the standard perturbation theory for the quantum Hamiltonian. There have been proposals in the literature for the non-perturbative contributions based on singularity cancellation with the perturbative contributions. We compute the quantum spectrum numerically with some high precisions for many cases of Planck constant. We find that there are also some higher order non-singular non-perturbative contributions, which are not captured by the singularity cancellation mechanism. We fix the first few orders formulas of such corrections for some well known local Calabi-Yau models.Comment: 47 pages, 3 figures. v2: journal version, typos correcte

Could the 21-cm absorption be explained by the dark matter suggested by 8^8Be transitions?

The stronger than expected 21-cm absorption was observed by EDGES recently, and another anomaly of $^8$Be transitions would be signatures of new interactions. These two issues may be related to each other, e.g., pseudoscalar $A$ mediated fermionic millicharged dark matter (DM), and the 21-cm absorption could be induced by photon mediated scattering between MeV millicharged DM and hydrogen. This will be explored in this paper. For fermionic millicharged DM $\bar{\chi} \chi$ with masses in a range of $2 m_A < 2 m_{\chi} < 3 m_A$, the p-wave annihilation $\bar{\chi} \chi \to A A$ would be dominant during DM freeze-out. The s-wave annihilation $\bar{\chi} \chi$ $\to A, \gamma$ $\to e^+ e^-$ is tolerant by constraints from CMB and the 21-cm absorption. The millicharged DM can evade constraints from direct detection experiments. The process of $K^+ \to \pi^+ \pi^0$ with the invisible decay $\pi^0 \to \bar{\chi} \chi$ could be employed to search for the millicharged DM, and future high intensity $K^+$ sources, such as NA62, will do the job.Comment: 6 pages, 2 figures, the accepted version, EPJ

Maximal violation of Clauser-Horne-Shimony-Holt inequality for two qutrits

Bell-Clauser-Horne-Shimony-Holt inequality (in terms of correlation functions) of two qutrits is studied in detail by employing tritter measurements. A uniform formula for the maximum value of this inequality for tritter measurements is obtained. Based on this formula, we show that non-maximally entangled states violate the Bell-CHSH inequality more strongly than the maximally entangled one. This result is consistent with what was obtained by Ac{\'{i}}n {\it et al} [Phys. Rev. A {\bf 65}, 052325 (2002)] using the Bell-Clauser-Horne inequality (in terms of probabilities).Comment: 6 pages, 3 figure