arXiv 2201.096322022-01-24hep-thgr-qc

双层上的三次闭弦场论

Cubic Closed String Field Theory on a Double Layer

Taejin Lee

备注：: 33 pages, 17 figures

摘要：

各种研究试图将Witten的三次开弦场论推广到三次闭弦场论，从而可以一致地描述低能区的爱因斯坦引力。在本研究中，我们提出了一个立方闭弦场论，引入双层来描述闭弦世界单作为Witten立方开弦世界单的扩展。我们将封闭弦世界单映射到复平面上，复平面的下半部分完全被弦世界单的扩展部分所覆盖。利用复平面上的格林函数，计算了Polyakov弦的路径积分，并由此导出了Neumann函数和顶点算子。我们得到了一个和两个字符串顶点（身份）以下的过程，最后立方字符串顶点操作。值得注意的是，所得到的立方弦散射振幅与爱因斯坦引力的立方引力子相互作用一致。因此，由此得到的立方闭弦场论一致地描述了爱因斯坦引力。我们还证明了第一量子化弦论的Kawai-Lewellen-Tye（KLT）关系在立方闭弦场论中也能得到体现。

英文摘要：

Various studies have attempted to extend the Witten's cubic open string field theory to the cubic closed string field theory, which may describe Einstein gravity in the low energy sector consistently. In the present study we propose a cubic closed string field theory, introducing a double layer to describe the closed string world-sheet as an extension of the open string world-sheet of the Witten's cubic open string. We mapped the closed string world-sheet onto the complex plane, of which the lower half plane is completely covered by the extended part of the string world-sheet. Using the Green's function on the complex plane, evaluated the Polyakov string path integral, from which we extracted the Neumann functions and the vertex operators. We obtained the one and two string vertices (identities) following this procedure and finally the cubic string vertex operator. It is notable that the obtained cubic string scattering amplitude coincide with the cubic graviton interaction of the Einstein gravity. Thus, the resultant cubic closed string field theory consistently describes the Einstein gravity. We also show that the Kawai-Lewellen-Tye (KLT) relations of the first quantized string theory may be manifested in the cubic closed string field theory.

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