近日，德国马克斯-普朗克物理研究所Stephan Stieberger团队研究了实投影平面上的超弦散射。相关论文于2025年5月27日发表在《高能物理杂志》上。

从定向平面的超弦散射需要考虑具有最低阶情况（在弦耦合常数中）的横帽的世界片上的弦振幅，该横帽具有实投影平面的拓扑结构。虽然在这项工作中，后者的振幅是针对微不足道的两点和两点情况制定的，但研究组超越了这些情况，从而解决了各种技术问题。后者包括将实射影平面上闭弦插入的复杂世界表积分简化为纯实开弦积分。 

因此，研究组发现n个闭弦在实射影平面上的散射可以用涉及2n个开弦的圆盘振幅来表示。在这项工作中，他们用纯旋量形式明确地计算出了n=3的情况，该情况可以写成两个（规范不变）六个开放弦振幅的线性组合。研究组还提出了在定向平面上构造闭弦耦合所需的这一结果的低能展开。

附：英文原文

Title: Superstring scattering on the real projective plane

Author: Bischof, Andreas, Stieberger, Stephan

Issue&Volume: 2025-05-27

Abstract: Superstring scattering from orientifold planes requires considering string amplitudes on world-sheets with crosscaps with the lowest order case (in string coupling constant) having the topology of the real projective plane. While amplitudes on the latter have been formulated for the trivial one- and two-point cases in this work we go beyond these cases thereby solving various technicalities. The latter include reducing the complex world-sheet integration of closed string insertions over the real projective plane to pure real open string integrals. As a result we find that scattering of n closed strings on the real projective plane can be expressed in terms of disk amplitudes involving 2n open strings. In this work we explicitly work out in pure spinor formalism the case n = 3 which can be written as a linear combination of two (gauge-invariant) six open string amplitudes. We also present the low-energy expansion of this result necessary to construct closed string couplings on orientifold planes.

DOI: 10.1007/JHEP05(2025)213

Source: https://link.springer.com/article/10.1007/JHEP05(2025)213