A BMS-invariant free scalar model

The BMS (Bondi-van der Burg-Metzner-Sachs) symmetry arises as the asymptotic symmetry of flat spacetime at null infinity. In particular, the BMS algebra for three dimensional flat spacetime (BMS$_3$) is generated by the super-rotation generators which form a Virasoro sub-algebra with central charge $c_L$, together with mutually-commuting super-translation generators. The super-rotation and super-translation generators have non-trivial commutation relations with another central charge $c_M$. In this paper, we study a free scalar theory in two dimensions exhibiting BMS$_3$ symmetry, which can also be understood as the ultra-relativistic limit of a free scalar CFT$_2$. Upon canonical quantization on the highest weight vacuum, the central charges are found to be $c_L=2$ and $c_M=0$. Because of the vanishing central charge $c_M=0$, the theory features novel properties: there exist primary states which form a multiplet, and the Hilbert space can be organized by an enlarged version of BMS modules dubbed the staggered modules. We further calculate correlation functions and the torus partition function, the later of which is also shown explicitly to be modular invariant.Comment: 59 pages, 5 figures. v2, minor revision: typos correted and some statement rephrase

The effect of TrkA signaling pathway on the expressions of TRPC1，TRPC3 in 6-hydroxydopamine lesioned rat treated by electroacupuncture

Objective: We investigate the effect of TrkA signaling pathway on the expressions of transient receptor potential channel in 6-hydroxydopamine(6-OHDA) lesioned rat treated by electroacupuncture and to explore the role of trkA signaling pathway and TRP subfamily in the pathogenesis of Parkinson's disease (PD), which would reveals the mechanisms of electroacupuncture (EA) neuroprotective effect. Methods:  The experimental models were established by unilateral injection of 6-OHDA into the left medial forebrain bundle (MFB).TrkA signaling pathway inhibitor K252a was infected into MFB through two small burr holes in the skull to block trkA signal.The change of TRPC1 and TRPC3 expressions was detected by use of immunohistochemistry and RT-PCR as well as TUNEL for cell apoptosis. Results:  The expressions of TRPC1 and TRPC3 in the substantia nigra (SN) of the 6-OHDA lesioned rat were significantly reduced. Compared with PD model group, TRPC1 and TRPC3 expressions were significantly increased in the EA group. There was no statistically significance in TRPC1 and TRPC3 expressions between K252a and PD model groups (P> 0.05). The number of apoptotic cells in SN increased 54.5% in the PD model rats, while positive apoptotic cells were significantly reduced in the EA group. There was no statistically significance in apoptotic cells between K252a and PD model groups (P>0.05). Conclusion:  TRPC1 and TRPC3 expressions downregulated in the SN of the 6-OHDA lesioned rat, which was accompanied by apoptosis increase in the SN. EA treatment could reverse this effect, and trkA signaling pathway inhibitors K252a can attenuate the neuroprotective effect of EA. It suggested that TRPC1 and TRPC3 may play an important role in the pathogenesis of PD, and certain TRPC subfamily expressions change may be associated with the pathogenesis of PD. Its expression might be subject to trkA signaling pathway, and this signal pathway may be the regulation target for EA neuroprotection.目的 观察trkA信号通路调控对电针处理的6-羟多巴胺(6-OHDA)损伤大鼠黑质瞬时受体势通道亚族TRPC1、TRPC3表达的影响，探讨trkA信号通路及TRPC1、TRPC3在帕金森病(PD)发病机制中的作用，揭示电针干预发挥神经保护效应的机制。方法 采用6-OHDA偏侧毁损方法建立PD大鼠模型，利用trkA信号通路抑制剂K252a立体定向注入左侧大鼠前脑束阻断trkA信号，用免疫组织化学法和RT-PCR法检测大鼠黑质区TRPC1、TRPC3基因表达的变化，并利用TUNEL检测黑质区细胞的凋亡情况。结果 模型组大鼠黑质区TRPC1和TRPC3基因表达显著减少，电针组大鼠黑质区TRPC1和TRPC3 基因表达较模型组显著增加；K252a组大鼠黑质区TRPC1、TRPC3表达明显减少，与模型组比较差异无统计学意义（P>0.05）。与电针组比较，模型组大鼠黑质区凋亡阳性细胞数目增加54.5%，电针组凋亡阳性细胞显著减少；而K252a组凋亡阳性细胞数目与模型组比较差异无统计学意义（P>0.05）。结论 6-OHDA损伤大鼠黑质区TRPC1、TRPC3基因表达下调，同时黑质区细胞凋亡增加。电针干预能够逆转这一变化，trkA信号通路抑制剂K252a能削弱电针的神经保护作用。TRPC某些亚族基因如TRPC1、TRPC3可能在PD的发病中扮演重要角色。TRPC1、TRPC3的表达可能受trkA信号通路的调控，该信号通路可能是电针治疗PD发挥神经保护作用的重要调节靶点

Shape-selective formation of monodisperse copper nanospheres and nanocubes via disproportionation reaction route and their optical properties

Synthesis of stable and monodisperse Cu nanocrystals of controlled morphology has been a long-standing challenge. In this Article, we report a facile disproportionation reaction approach for the synthesis of such nanocrystals in organic solvents. Either spherical or cubic shapes can be produced, depending on conditions. The typical Cu nanospheres are single crystals with a size of 23.4 ± 1.5 nm, and can self-assemble into three-dimensional (3D) nanocrystal superlattices with a large scale. By manipulating the chemical additives, monodisperse Cu nanocubes with tailorable sizes have also been obtained. The probable formation mechanism of these Cu nanocrystals is discussed. The narrow size distribution results in strong surface plasmon resonance (SPR) peaks even though the resonance is located in the interband transition region. Double SPR peaks are observed in the extinction spectra for the Cu nanocubes with relative large sizes. Theoretical simulation of the extinction spectra indicates that the SPR band located at longer wavelengths is caused by assembly of Cu nanocubes into more complex structures. The synthesis procedure that we report here is expected to foster systematic investigations on the physical properties and self-assembly of Cu nanocrystals with shape and size singularity for their potential applications in photonic and nanoelectronic devices. © 2014 American Chemical Society