Closed-string amplitude recursions from the Deligne associator

Summary

The article discusses the recursion relations for closed-string tree-level amplitudes using the Deligne associator. The authors establish a recursive algorithm for computing L-point closed-string amplitudes from (L-1)-point amplitudes, utilizing the Deligne associator and the single-valued map.

Highlights

• The Deligne associator is used to establish a recursive algorithm for closed-string tree-level amplitudes.
• The single-valued map is utilized to relate open-string and closed-string amplitudes.
• The recursion relations are based on the Knizhnik-Zamolodchikov (KZ) equation.
• The authors use Selberg integrals and their limiting behavior to derive the recursion relations.
• The results provide a new understanding of the structure of closed-string amplitudes.
• The Deligne associator plays a crucial role in the recursion relations.
• The single-valued map is essential for relating open-string and closed-string amplitudes.

Key Insights

• The Deligne associator is a mathematical object that encodes the monodromy of the KZ equation, allowing for the establishment of recursion relations for closed-string tree-level amplitudes.
• The single-valued map is a crucial tool for relating open-string and closed-string amplitudes, enabling the computation of closed-string amplitudes from open-string amplitudes.
• The recursion relations derived in the article provide a new understanding of the structure of closed-string amplitudes, shedding light on the underlying mathematical structure of string theory.
• The use of Selberg integrals and their limiting behavior is essential for deriving the recursion relations, demonstrating the importance of mathematical techniques in understanding physical systems.
• The results of the article have significant implications for our understanding of string theory, providing a new tool for computing closed-string amplitudes and shedding light on the underlying structure of the theory.
• The Deligne associator and the single-valued map are fundamental objects in the theory of closed-string amplitudes, playing a crucial role in the recursion relations and the computation of amplitudes.
• The article demonstrates the power of mathematical techniques in understanding physical systems, highlighting the importance of interdisciplinary research in advancing our understanding of the universe.

Mindmap

Citation

Baune, K., Broedel, J., & Zerbini, F. (2024). Closed-string amplitude recursions from the Deligne associator (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.17579