论文标题
Thomas-White头重力的分级扩展
The Graded Extension of Thomas-Whitehead Gravity
论文作者
论文摘要
最近将Thomas-Whitehead（TW）重力作为D维歧管上引入了重力理论，该理论通过使用Thomas-Whitehead Connection将重新聚集的不变性嵌入重力功能中。该D维理论中的投影不变性与在字符串理论中发现的Virasoro coadexhexhexhexhexhexhexhexhexhexhexhexhex元素是连接的组成部分之一，$ \ Mathcal {d} _ {Ab {ab} $与Virasoro Algebra的coadexexhoint元素直接相关。 TW重力利用了动作功能中的投影高斯 - 骨网术语，该函数使理论可以在$ \ Mathcal {d} _ {ab} $消失的极限上崩溃到爱因斯坦的一般相对性理论。在本说明中，我们在DeWitt Supermanifold的框架内开发了TW重力的分级扩展。我们构建了Lagrangian的超级TW重力，给出了经典场方程的详细推导，并讨论了投射连接的分级扩展，以此作为对TW-SuperGravity的未来理解（表现出超对称性）的未来理解及其与Super-Virasoro Algebra的关系。
Thomas-Whitehead (TW) gravity was recently introduced as a projective gauge theory of gravity over a d-dimensional manifold that embeds reparameterization invariance into the action functional for gravitation through the use of the Thomas-Whitehead connection. The projective invariance in this d-dimensional theory enjoys an intimate relationship with the Virasoro coadjoint elements found in string theory as one of the components of the connection, $\mathcal{D}_{ab}$, is directly related to the coadjoint elements of the Virasoro algebra. TW Gravity exploits projective Gauss-Bonnet terms in the action functional which allows the theory to collapse to Einstein's theory of General Relativity in the limit that $\mathcal{D}_{ab }$ vanishes. In this note we develop the graded extension of TW Gravity, Super TW Gravity, in the framework of a DeWitt supermanifold. We construct the Lagrangian for Super TW Gravity, give a detailed derivation of the classical field equations and discuss the graded extension of the projective connection as a prelude to a future understanding of TW-Supergravity (which has manifest supersymmetry) and its relationship to the Super-Virasoro algebra.
