120014994
Complete cscK Metrics on the Local Models of the Conifold Transition
In this paper, we construct complete constant scalar curvature Kähler (cscK) metrics on the complement of the zero section in the total space of $${\mathcal{O}(-1)^{\oplus2}}$$O(-1)⊕2 over $${\mathbb{P}^{1}}$$P1, which is biholomorphic to the smooth part of the cone C0 in $${\mathbb{C}^{4}}$$C4 defined by equation $${\Sigma_{i=1}^{4} w_{i}^{2}=0}$$Σi=14wi2=0. On its small resolution and its deformation, we also consider complete cscK metrics and find that if the cscK metrics are homogeneous, then they must be Ricci-flat.
54679841
Twistor geometry of Riemannian 4-manifolds by moving frames
In this paper, we characterize Riemannian 4-manifold in terms of its almost Hermitian twistor spaces $(Z,g_t,\mathbb{J}_{\pm})$. Some special metric conditions (including Balanced metric condition, first Gauduchon metric condition) on $(Z,g_t,\mathbb{J}_{\pm})$ are studied. For the first Chern form of a natural unitary connection on the vertical tangent bundle over the twistor space $Z$, we can recover J. Fine and D. Panov's result on the condition of the first Chern form being symplectic and P. Gauduchon's result on the condition of the first Chern form being a (1,1)-form respectively, by using the method of moving frames.
115168215
Balanced metrics on non-Kahler Calabi-Yau threefolds
We construct balanced metrics on the family of non-K\"ahler Calabi-Yau threefolds that are obtained by smoothing after contracting $(-1,-1)$-rational curves on K\"ahler Calabi-Yau threefold. As an application, we construct balanced metrics on complex manifolds diffeomorphic to connected sum of $k\geq 2$ copies of $S^3\times S^3$.
14167369
The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation
The purpose of this paper is to solve a problem posed by Strominger in constructing smooth models of superstring theory with flux. These are given by non-Kahler manifolds with torsion.
117850186
Existence of Supersymmetric Hermitian Metrics with Torsion on Non-Kaehler Manifolds
We proved the existence of supersymmetric Hermitian metrics with torsion on a class of non-Kaehler manifolds.
16780880
Local Heterotic Torsional Models
We present a class of smooth supersymmetric heterotic solutions with a non-compact Eguchi-Hanson space. The non-compact geometry is embedded as the base of a six-dimensional non-Kähler manifold with a non-trivial torus fiber. We solve the non-linear anomaly equation in this background exactly. We also define a new charge that detects the non-Kählerity of our solutions.
119237185
Study of the electromagnetic transitions $J/\psi \rightarrow P l^+l^-$ and probe dark photon
We study the electromagnetic Dalitz decay modes of $J/\psi \rightarrow P l^+l^-$ ($P= \pi^0$, $\eta$ or $\eta^\prime$). In these decays, the lepton pairs are formed by internal conversion of an intermediate virtual photon with invariant mass $m_{l^+l^-}$. Study of the effective-mass spectrum of the $l^+l^-$ will shed light on the dynamic transition form factor $F_{J/\psi P}(q^2)$ ($q^2 = m^2_{l^+l^-}$), which characterizes the electromagnetic structure arising at the vertex of the transition $J/\psi$ to pseudoscalars. We also discuss the direct productions of a GeV scale vector $U$ boson in these processes $J/\psi \rightarrow PU$ ($U\rightarrow l^+l^-$). It is responsible for mediating a new $U(1)_d$ interaction, as recently exploited in the context of weakly interacting massive particle dark matter. 
In this paper, we firstly use the usual pole approximation for the form factor to estimate the decay rate of $J/\psi \rightarrow P l^+l^-$ in the standard model. Then the reach of searching for the dark photon is estimated. We suggest that these Dalitz decays can be used to search for the light $U$ boson in the BESIII experiment with a huge $J/\psi$ data set.