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arXiv 1902.00263hep-th
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弦场论作为世界片UV调节器

String Field Theory as World-sheet UV Regulator

Ashoke Sen

摘要:

即使在树的层次上,第一个量子化的弦论也有明显的短距离奇异性,这与顶点算子的碰撞有关,使我们无法直接进行各种量的数值计算。例子包括一般外动量的弦论S-矩阵和在世界片理论的边缘变形下的弦论谱的计算。前者要求我们通过解析延拓或作为复化模空间中围道积分的极限来定义S-矩阵,而后者要求我们在中间步骤使用紫外截止。相比之下,弦场论就不会有这样的分歧。在本文中,我们将展示如何弦场论可以用来产生一个明确的算法计算树水平振幅在任何弦论,不遭受任何短距离发散从整合的世界片变量。我们还利用弦场论计算了弦态在边缘形变下的二阶质量位移,而不必在中间步骤使用任何截止。我们在一大类弦场论中进行了分析,从而表明,最终结果与进入弦场论公式的额外数据无关。我们还评论了这种分析的推广到更高的属振幅。

英文摘要:

Even at tree level, the first quantized string theory suffers from apparent short distance singularities associated with collision of vertex operators that prevent us from straightforward numerical computation of various quantities. Examples include string theory S-matrix for generic external momenta and computation of the spectrum of string theory under a marginal deformation of the world-sheet theory. The former requires us to define the S-matrix via analytic continuation or as limits of contour integrals in complexified moduli space, while the latter requires us to use an ultraviolet cut-off at intermediate steps. In contrast, string field theory does not suffer from such divergences. In this paper we show how string field theory can be used to generate an explicit algorithm for computing tree level amplitudes in any string theory that does not suffer from any short distance divergence from integration over the world-sheet variables. We also use string field theory to compute second order mass shift of string states under a marginal deformation without having to use any cut-off at intermediate steps. We carry out the analysis in a broad class of string field theories, thereby making it manifest that the final results are independent of the extra data that go into the formulation of string field theory. We also comment on the generalization of this analysis to higher genus amplitudes.

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。

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