具有Englert通量的超对称M2-branes与单群PSL（2，7）
Supersymmetric M2-branes with Englert Fluxes and the simple group PSL(2,7)
摘要：
引入了一类新的7维d=11超引力M2膜解，其中包含了服从Englert方程的内通量.在这种背景下，Killing旋量存在的一个简单的标准。本文将Englert方程看作是d=3的Beltrami方程在d=7时的推广，并对它进行了相应的推导。所有最小d=7超引力的2-膜解都可以提升到d=11，并具有N > 4或N = 4的超对称性。证明了单群PSL（2，7）在d=7时是晶体学的，对A7根格有积分作用.通过这个点群和用A7根格取代R7得到的T7环面，我们能够构造具有恩格勒通量和N < 4的新的M2膜。特别地，我们在这里展示了一个N=1的解决方案，依赖于4-参数，并承认一个大的非阿贝尔离散对称，即G21 = Z3半直积与Z7 =子群的PSL（2，7）。d=3的对偶场论具有相同的对称性，并具有复杂的非线性相互作用。
英文摘要：
A new class is introduced of M2-branes solutions of d=11 supergravity that include internal fluxes obeying Englert equation in 7-dimensions. A simple criterion for the existence of Killing spinors in such backgrounds is established. Englert equation is viewed as the generalization to d=7 of Beltrami equation defined in d=3 and it is trated accordingly. All 2-brane solutions of minimal d=7 supergracity can be uplifted to d=11 and have N > 4 or N = 4 supersymmetry. It is shown that the simple group PSL(2,7) is crystallographic in d=7 having an integral action on the A7 root lattice. By means of this point-group and of the T7 torus obtained quotiening R7 with the A7 root lattice we were able to construct new M2 branes with Englert fluxes and N < 4. In particular we exhibit here an N=1 solution depending on 4-parameters and admitting a large non abelian discrete symmetry, namely G21 = Z3 semidirect product with Z7 = subgroup of PSL(2,7). The dual d=3 field theories have the same symmetries and have complicated non linear interactions.
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