One-loop Double Copy Relation from Twisted (Co)homology

2024/03/08 by Pouria Mazloumi, Stephan Stieberger, Mazloumi, Pouria +1 · 5 citations
Computer Science · Medicine · #Advanced Neuroimaging Techniques and Applications #Algebraic Geometry (math.AG) #Cancer Treatment and Pharmacology #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2403.05208

openalex publication_date 2024/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a geometric relation between closed and open string amplitudes at one-loop. After imposing a homological splitting on the world-sheet torus twisted intersection theory is used to establish a one-loop double copy relation. The latter expresses a closed string amplitude by a pair of open string amplitudes and twisted intersection numbers. These inner products on the vector space of allowed differential forms are related to the twisted homology and cohomology groups associated with the Riemann-Wirtinger integral.

Cited by

• Twisted de Rham theory for string double copy in AdS
• A construction of single-valued elliptic polylogarithms
• Superstring amplitudes from the field-theory limit: an n-point map at one loop
• One-loop four-graviton string amplitude at finite α'
• Associators for AdS string amplitude building blocks

Related

• Twisted de Rham theory for string double copy in AdS
• A double copy from twisted (co)homology at genus g
• A modern approach to String Amplitudes and Intersection Theory
• One-loop Double Copy Relation in String Theory
• Intersections of Twisted Forms: New Theories and Double Copies