arXiv 2102.005552021-02hep-thmath.DG

作为广义测地线的经典世界体积

Classical worldvolumes as generalised geodesics

Charles Strickland-Constable

备注：: 29 pages

摘要：

自平行向量场的积分曲线是测地线，这是一个标准的结果，对于零向量和类时向量，测地线是广义相对论中自由下落粒子的路径。我们引入了一个定义的“自动平行”广义向量场，并表明，它给出了类似的声明，为经典的worldvolumes的字符串和膜在任意背景场配置。这似乎给出了弦和膜的世界体积方程的统一描述，类似于广义几何提供最大超引力理论的统一描述。我们详细介绍了$O(10,10)$广义几何中弦世界面的情况和限制在$SL(5,\mathbb{R})\times\mathbb{R}^+$广义几何四维中的M2膜。一个关键的量是沿着广义切向量的共轭动量的无穷小流，它等同于哈密顿量的梯度，被视为时空上的函数。

英文摘要：

It is a standard result that the integral curves of an auto-parallel vector field are geodesics which, for null and timelike vectors, are the paths of freely-falling particles in general relativity. We introduce a definition of an "auto-parallel" generalised vector field and show that it gives the analogous statements for the classical worldvolumes of strings and branes in arbitrary background field configurations. This appears to give a unified description of the worldvolume equations of strings and branes, similar to the way that generalised geometry provides a unified description of maximal supergravity theories. We present details of the cases of string worldsheets in $O(10,10)$ generalised geometry and M2 branes restricted to the four dimensions of $SL(5,\mathbb{R})\times\mathbb{R}^+$ generalised geometry. A key quantity is the infinitesimal flow of the conjugate momentum along the generalised tangent vector, which is equated to the gradient of the Hamiltonian, viewed as a function on spacetime.

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：

相关论文