2-极小D=7超引力的Arnold-Beltrami通量膜
2-branes with Arnold-Beltrami Fluxes from Minimal D=7 Supergravity
摘要：
我们将这篇论文描述为从流体力学到超重力的感伤之旅。三维Beltrami方程在不可压缩流体力学中起着关键的作用，它与七维最小超引力有着不可怀疑的联系。我们证明了只有D=7的超引力理论，而没有其他具有相同场含量但拉格朗日系数不同的理论，在横向方向上的Arnold-Beltrami通量被打开的情况下，存在精确的双膜解. Beltrami方程的解有丰富的离散群，即三环面上 *d算子的本征函数，都是通过这个新发现的标记注入膜世界的。一个新的相当广泛的运动场为超引力及其在三维空间中的对偶规范理论开辟了，在那里，所有的经典场和所有的量子复合算符都将被指定为离散晶体群的不可约表示。
英文摘要：
We describe this paper as a Sentimental Journey from Hydrodynamics to Supergravity. Beltrami equation in three dimensions that plays a key role in the hydrodynamics of incompressible fluids has an unsuspected relation with minimal supergravity in seven dimensions. We show that just D=7 supergravity and no other theory with the same field content but different coefficients in the lagrangian, admits exact two-brane solutions where Arnold-Beltrami fluxes in the transverse directions have been switched on. The rich variety of discrete groups that classify the solutions of Beltrami equation, namely the eigenfunctions of the *d operator on a three-torus, are by this newly discovered token injected into the brane world. A new quite extensive playing ground opens up for supergravity and for its dual gauge theories in three dimensions, where all classical fields and all quantum composite operators will be assigned to irreducible representations of discrete crystallographic groups.
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