arXiv 2103.136822021-03hep-th

有边界条件下$α'$阶弦论的有效action

Effective action of string theory at order $α'$ in the presence of boundary

Mohammad R. Garousi

备注：: 30 pages, Latex file, no figure; v7:extend the cosmological reduction to the general one-dimensional reduction which includes timelike or spacelike boundary
DOI：: 10.1140/epjc/s10052-021-09952-6

摘要：

最近，利用临界维数下的弦论有效作用量与背景无关的假设，通过在背景为圆形时施加$O(1,1)$对称性，在无边界时空流形中再现了$α'$阶玻色弦论的经典壳层有效作用量，直到总参数。在边界存在的情况下，我们考虑一个具有边界和圆的背景，使得边界的单位法向量与圆无关。然后，$O(1,1)$对称性可以在不使用最低阶运动方程的情况下固定体作用量。此外，上述约束条件和最小作用量原理在边界存在的约束可以固定边界作用量，多达五个边界参数。在最小作用量原理中，我们假定在边界上，不仅无质量场的值是任意的，而且它们的一阶导数的值也是任意的。我们还观察到，在Hawking-Gibbons边界项存在的情况下，首阶作用量的宇宙学/一维约化产生零边界作用量。强加这作为另一个约束的边界耦合顺序$α'$，我们发现边界行动两个参数。对于这两个参数的特定值，边界中的重力耦合变为Chern-Simons重力加上另一项，该项具有外部曲率的Laplacian。

英文摘要：

Recently, using the assumption that the string theory effective action at the critical dimension is background independent, the classical on-shell effective action of the bosonic string theory at order $α'$ in a spacetime manifold without boundary has been reproduced, up to an overall parameter, by imposing the $O(1,1)$ symmetry when the background has a circle. In the presence of the boundary, we consider a background which has boundary and a circle such that the unit normal vector of the boundary is independent of the circle. Then the $O(1,1)$ symmetry can fix the bulk action without using the lowest order equation of motion. Moreover, the above constraints and the constraint from the principle of the least action in the presence of boundary can fix the boundary action, up to five boundary parameters. In the least action principle, we assume that not only the values of the massless fields but also the values of their first derivatives are arbitrary on the boundary. We have also observed that the cosmological/one-dimensional reduction of the leading order action in the presence of the Hawking-Gibbons boundary term, produces zero boundary action. Imposing this as another constraint on the boundary couplings at order $α'$, we find the boundary action up to two parameters. For a specific value for these two parameters, the gravity couplings in the boundary become the Chern-Simons gravity plus another term which has the Laplacian of the extrinsic curvature.

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