arXiv 1606.052392016-06hep-thcond-mat.other

非常规超对称性的动力学内容

Dynamical Contents of Unconventional Supersymmetry

Alfredo Guevara, Pablo Pais, Jorge Zanelli

备注：: 17 pages. Accepted version for publication in JHEP
发表信息：: JHEP (2016) 2016: 85
DOI：: 10.1007/JHEP08(2016)085

摘要：

狄拉克哈密顿形式主义被应用到一个系统在$(2+1)$ -维组成的狄拉克场$ψ$最低限度地耦合到陈-西蒙斯$U(1)$和$SO(2,1)$连接，$A$和$ω$，分别。这个理论与超对称的陈-西蒙斯形式有关，其中引力子被投影出来（非常规超对称性），并且在平坦背景的情况下，对应于石墨烯的低能极限。第一类和第二类约束之间的分离进行明确的，和两个场方程和规范对称性的拉格朗日形式完全恢复。在一般部门的理论的自由度表明，传播状态对应于费米模式的石墨烯片的几何形状和非动态电磁场确定的背景。这是显示为以下典型部门：i）共形不变的通用描述，其中的旋量场和dreibein是本地重新标度; ii）一个特定的配置狄拉克费米子符合其自旋，其中Weyl对称性交换的时间reparametrizations; iii）真空部门$ψ=0$，这是感兴趣的微扰理论。对于后者，分析适用于有边界流形的情形，并找到相应的Dirac括号和中心扩张电荷代数.最后，对规范群的$SU(2)$推广作了简要的处理，得到了自由度的类似结论.

英文摘要：

The Dirac Hamiltonian formalism is applied to a system in $(2+1)$-dimensions consisting of a Dirac field $ψ$ minimally coupled to Chern-Simons $U(1)$ and $SO(2,1)$ connections, $A$ and $ω$, respectively. This theory is connected to a supersymmetric Chern-Simons form in which the gravitino has been projected out (unconventional supersymmetry) and, in the case of a flat background, corresponds to the low energy limit of graphene. The separation between first-class and second-class constraints is performed explicitly, and both the field equations and gauge symmetries of the Lagrangian formalism are fully recovered. The degrees of freedom of the theory in generic sectors shows that the propagating states correspond to fermionic modes in the background determined by the geometry of the graphene sheet and the nondynamical electromagnetic field. This is shown for the following canonical sectors: i) a conformally invariant generic description where the spinor field and the dreibein are locally rescaled; ii) a specific configuration for the Dirac fermion consistent with its spin, where Weyl symmetry is exchanged by time reparametrizations; iii) the vacuum sector $ψ=0$, which is of interest for perturbation theory. For the latter the analysis is adapted to the case of manifolds with boundary, and the corresponding Dirac brackets together with the centrally extended charge algebra are found. Finally, the $SU(2)$ generalization of the gauge group is briefly treated, yielding analogous conclusions for the degrees of freedom.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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