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String correlators: recursive expansion, integration-by-parts and scattering equations

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  • Published:11 September 2019
  • Volume 2019,article number85,(2019)
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String correlators: recursive expansion, integration-by-parts and scattering equations
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  • Song He1,2,
  • Fei Teng3&
  • Yong Zhang1,2

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Apreprint versionof the article is available at arXiv.

Abstract

We further elaborate on the general construction proposed in [1], which connects, via tree-level double copy, massless string amplitudes with color-ordered QFT amplitudes that are given by Cachazo-He-Yuan formulas. The current paper serves as a detailed study of the integration-by-parts procedure for any tree-level massless string correlator outlined in the previous letter. We present two new results in the context of heterotic and (compactified) bosonic string theories. First, we find a new recursive expansion of any multitrace mixed correlator in these theories into a logarithmic part corresponding to the CHY integrand for Yang-Mills-scalar amplitudes, plus correlators with the total number of traces and gluons decreased. By iterating the expansion, we systematically reduce string correlators with any number of subcycles to linear combinations of Parke-Taylor factors and similarly for the case with gluons. Based on this, we then derive a CHY formula for the corresponding (DF)2+ YM +ϕ3amplitudes. It is the first closed-form result for such multitrace amplitudes and thus greatly extends our result for the single-trace case. As a byproduct, it gives a new CHY formula for all Yang-Mills-scalar amplitudes. We also study consistency checks of the formula such as factorizations on massless poles.

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Authors and Affiliations

  1. CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Song He & Yong Zhang

  2. School of Physical Sciences, University of Chinese Academy of Sciences, No.19A Yuquan Road, Beijing, 100049, China

    Song He & Yong Zhang

  3. Department of Physics and Astronomy, Uppsala University, 75108, Uppsala, Sweden

    Fei Teng

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Correspondence to Fei Teng.

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ArXiv ePrint:1907.06041

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He, S., Teng, F. & Zhang, Y. String correlators: recursive expansion, integration-by-parts and scattering equations. J. High Energ. Phys.2019,85 (2019). https://doi.org/10.1007/JHEP09(2019)085

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  • Received:29 July 2019

  • Revised:03 September 2019

  • Accepted:03 September 2019

  • Published:11 September 2019

  • DOI:https://doi.org/10.1007/JHEP09(2019)085

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Keywords

  • Scattering Amplitudes
  • Bosonic Strings
  • Gauge Symmetry
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