Search

In this note, we study the singular mean field equation defined on a Riemann surface with a sign-changing potential function. We prove if some singular sources happen to be placed on the zero-level curve of the potential function, a priori estimate can still be obtained. As a consequence of this estimate, existence and multiplicity results can still be obtained based on the topology of the manifold.

Possible light bosonic dark matter interactions with the Standard Model photon have been searched by microwave resonant cavities. In this paper, we demonstrate the cryogenic readout system calibration of a 7.138 GHz copper cavity with a loaded quality factor $Q_l=10^4$, operated at 22 mK temperature based on a dilution refrigerator. Our readout system consists of High Electron Mobility Transistors as cryogenic amplifiers at 4 K, plus room-temperature amplifiers and a spectrum analyzer for signal power detection. We test the system with a superconducting two-level system as a single-photon source in the microwave frequency regime and report an overall 95.6 dB system gain and -71.4 dB attenuation in the cavity's input channel. The effective noise temperature of the measurement system is 7.5 K., Comment: 7 pages, 5 figures, version to appear in CPC

The dark photon is a promising candidate for the dark matter which comprises most of the matter in our visible Universe. Via kinetic mixing with the Standard Model it can also be resonantly converted to photons in an electromagnetic cavity, offering novel experimental possibilities for the discovery and study of dark matter. We report the results of a pathfinder dark photon dark matter cavity search experiment performed at Hunan Normal University and the Institute of Physics, Chinese Academy of Sciences, representing the first stage of the APEX (Axion and dark Photon EXperiment) program. Finding no statistically significant excess, we place an upper limit on the kinetic mixing parameter $|\chi|<3.7\times 10^{-13}$ around $m_A\simeq 29.5$ $\mu$eV at 90% confidence level. This result exceeds other constraints on dark photon dark matter in this frequency range by roughly an order of magnitude., Comment: 5 pages, 4 figures. Updated to match journal version

We develop generalized no-scale supergravity models of inflation, and then study the corresponding cosmological predictions as well as the formation of primordial black holes (PBHs) and scalar-induced gravitational waves (SIGWs). With a new parameter $0

In a recent series of important works \cite{wei-zhang-1,wei-zhang-2,wei-zhang-3}, Wei-Zhang proved several vanishing theorems for non-simple blow-up solutions of singular Liouville equations. It is well known that a non-simple blow-up situation happens when the spherical Harnack inequality is violated near a quantized singular source. In this article, we further strengthen the conclusions of Wei-Zhang by proving that if the spherical Harnack inequality does hold, there exist blow-up solutions with non-vanishing coefficient functions., Comment: 13 pages

It is well-known that three-family supersymmetric Pati-Salam models from intersecting D6-branes, where either one or both of the ${\rm U}(2)$ gauge factors are replaced by a ${\rm USp}(2)$ group, are quite scarce. In order to construct all such kind of models with generic additional gauge symmetries, we fix the observable sectors and study all the possible hidden sectors. Thus, we are able to completely determine all types of such kind of the inequivalent models on a $\mathbb{T}^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ orientifold from IIA string theory. We find the gauge coupling relations to be highly sensitive to the variations in the hidden sector. One of the models exhibits the gauge coupling unification for a particular solution at the string scale. In addition, we perform scan on the hidden sector variations for the models presented in arXiv:2112.09632, whose gauge coupling relations are still preserved. Thus, we fix the gap in the previous study and complete the model building for all the inequivalent models., Comment: 25+4 pages, 6 figures and 15 tables; added machine learning details; published version. arXiv admin note: text overlap with arXiv:2212.09644

We construct new three-family ${\cal N}=1$ supersymmetric Pati-Salam models from intersecting D6-branes with original gauge group ${\rm U}(4)_C \times {\rm USp}(2)_L \times {\rm U}(2)_R$ on a Type IIA $\mathbb{T}^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ orientifold. We find that replacing a ${\rm U}(2)$ with a ${\rm USp}(2)$ group severely restricts the number of three-generation supersymmetric models such that there are only five inequivalent models. Exchanging the left and right sectors, we obtain five dual models with gauge group ${\rm U}(4)_C \times {\rm U}(2)_L \times {\rm USp}(2)_R$. These ten models have different gauge coupling relations at string scale. The highest wrapping number is 4, and one of the models contains no filler O6-planes. Moreover, we discuss in detail the particle spectra, the composite particles through strong coupling dynamics, and the exotic particle decouplings. Also, we study how to realize the string-scale gauge coupling relations in some models., Comment: 32 pages, 3 figures, published version

We have constructed all the three-family ${\cal N} = 1$ supersymmetric Pati-Salam models from intersecting D6-branes, and obtained 33 independent models in total. But how to realize the string-scale gauge coupling relations in these models is a big challenge. We first discuss how to decouple the exotic particles in these models. In addition, we consider the adjoint chiral mulitplets for $SU(4)_C$ and $SU(2)_L$ gauge symmetries, the Standard Model (SM) vector-like particles from D6-brane intersections, as well as the vector-like particles from the ${\cal N}=2$ subsector. We show that the gauge coupling relations at string scale can be achieved via two-loop renormalization group equation running for all these supersymmetric Pati-Salam models. Therefore, we propose a concrete way to obtain the string-scale gauge coupling realtions for the generic intersecting D-brane models., Comment: 40 pages, 23 figures, and 40 tables; references added, published version

In this article we study bubbling solutions of regular $SU(3)$ Toda systems defined on a Riemann surface. There are two major difficulties corresponding to the profile of bubbling solutions: partial blowup phenomenon and bubble accumulation. We prove that when both parameters tend to critical positions, if there is one fully bubbling blowup point, then under one curvature assumption, all the blowup solutions near a blowup point satisfy a spherical Harnack inequality, which completely rules out the bubble-accumulation phenomenon. This fact is crucial for a number of applications., Comment: 42 pages. arXiv admin note: text overlap with arXiv:2202.10825

We propose the generic no-scale inflation inspired from string theory compactifications. We consider the K\"ahler potentials with an inflaton field $\varphi$, as well as one, two, and three K\"ahler moduli. Also, we consider the renormalizable superpotential of $\varphi$ in general. We study the spectral index and tensor-to-scalar ratio in details, and find the viable parameter spaces which are consistent with the Planck and BICEP/Keck experimental data on the cosmic microwave background (CMB). The spectral index is $n_s\simeq 1-2/N \sim 0.965$ for all models, and the tensor-to-scalar ratio $r$ is $r\simeq12/N^2$, $ 83/N^4$ and $ 4/N^2$ for the one, two and three moduli models, respectively. The particular $r$ for two moduli model comes from the contributions of the non-negligible higher order term in potential. In the three moduli model, the scalar potential is similar to the global supersymmetry, but the K\"ahler potential is different. The E-model with $\alpha=1$ and T-model with $\alpha=1/3$ can be realized in the one modulus model and the three moduli model, respectively. Interestingly, the models with quadratic and quartic potentials still satisfy the current tight bound on $r$ after embedding into no-scale supergravity., Comment: 40 pages, 32 figures, 2 tables; v2: pubulished version, references added

All the possible three-family ${\cal N}=1$ supersymmetric Pati-Salam models constructed with intersecting D6-branes from Type IIA orientifolds on $T^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ are recently presented in arXiv: 2112.09632. Taking models with largest wrapping number $5$ and approximate gauge coupling unification at GUT scale as examples, we show string scale gauge coupling unification can be realized through two-loop renormalization group equation running by introducing seven pairs of vector-like particles from ${\cal N}=2$ sector. The number of these introduced vector-like particles are fully determined by the brane intersection numbers while there are two D6-brane parallel to each other along one two-torus. We expect this will solve the gauge coupling unification problem in the generic intersecting brane worlds by introducing vector-like particles that naturally included in the ${\cal N}=2$ sector., Comment: 3 figures