Loops in twistor space

2004/10/31 by Iosif Bena, Zvi Bern, David A. Kosower +1 · 7 citations
Computer Science · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computer science #Mathematical physics #Mathematics #Numerical Methods and Algorithms #Parallel Computing and Optimization Techniques #Space (punctuation) #Twistor space #Twistor theory #hep-th

paper · pdf · doi:10.1103/physrevd.71.106010

published as Phys.Rev. D71 (2005) 106010 · 21 pages, TeX. v3. missing citations added. v4. subtlety with the i εprescription clarified

arxiv created 2005/01/12 · openalex publication_date 2005/05/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We elucidate the one-loop twistor-space structure corresponding to momentum-space maximally helicity-violating diagrams. We also discuss the infrared divergences, and argue that only a limited set of maximally helicity-violating diagrams contain them. We show how to introduce a twistor-space regulator corresponding to dimensional regularization for the infrared-divergent diagrams. We also evaluate explicitly the ``holomorphic anomaly'' pointed out by Cachazo, Svr\ifmmode \checkc\else \vc\fiek, and Witten, and use the result to define modified differential operators which can be used to probe the twistor-space structure of one-loop amplitudes.

Citations

• Infinities within graviton scattering amplitudes
• Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• A Googly Amplitude from the B-model in Twistor Space
• Perturbative Gauge Theory As A String Theory In Twistor Space

Cited by

• Computing one-loop amplitudes from the holomorphic anomaly of unitarity cuts
• Marginal deformations of N=4 SYM from open/closed twistor strings
• Maximally helicity-violating diagrams in twistor space and the twistor action
• Recursion relations for gauge theory amplitudes with massive particles
• The rational parts of one-loop QCD amplitudes I: The general formalism
• Twistor transform of all tree amplitudes in N=4 SYM theory
• Numerical evaluation of six-photon amplitudes