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Towards the n-point one-loop superstring amplitude. Part II. Worldsheet functions and their duality to kinematics

Towards the n-point one-loop superstring amplitude. Part II. Worldsheet functions and their duality to kinematics
Towards the n-point one-loop superstring amplitude. Part II. Worldsheet functions and their duality to kinematics

This is the second installment of a series of three papers in which we describe a method to determine higher-point correlation functions in one-loop open-superstring amplitudes from first principles. In this second part, we study worldsheet functions defined on a genus-one surface built from the coefficient functions of the Kronecker-Einsenstein series. We construct two classes of worldsheet functions whose properties lead to several simplifying features within our description of one-loop correlators with the pure-spinor formalism. The first class is described by functions with prescribed monodromies, whose characteristic shuffle-symmetry property leads to a Lie-polynomial structure when multiplied by the local superfields from part I of this series. The second class is given by so-called generalized elliptic integrands (GEIs) that are constructed using the same combinatorial patterns of the BRST pseudo-invariant superfields from part I. Both of them lead to compact and combinatorially rich expressions for the correlators in part III. The identities obeyed by the two classes of worldsheet functions exhibit striking parallels with those of the superfield kinematics. We will refer to this phenomenon as a duality between worldsheet functions and kinematics.

Conformal Field Theory, Superstrings and Heterotic Strings
1126-6708
1-63
Mafra, Carlos R.
5a40c14f-0ddb-4c0c-9ce5-acabc537cd01
Schlotterer, Oliver
d30fbe50-b9eb-489a-ad79-0dd212ef4e0e
Mafra, Carlos R.
5a40c14f-0ddb-4c0c-9ce5-acabc537cd01
Schlotterer, Oliver
d30fbe50-b9eb-489a-ad79-0dd212ef4e0e

Mafra, Carlos R. and Schlotterer, Oliver (2019) Towards the n-point one-loop superstring amplitude. Part II. Worldsheet functions and their duality to kinematics. Journal of High Energy Physics, 2019 (8), 1-63, [91]. (doi:10.1007/JHEP08(2019)091).

Record type: Article

Abstract

This is the second installment of a series of three papers in which we describe a method to determine higher-point correlation functions in one-loop open-superstring amplitudes from first principles. In this second part, we study worldsheet functions defined on a genus-one surface built from the coefficient functions of the Kronecker-Einsenstein series. We construct two classes of worldsheet functions whose properties lead to several simplifying features within our description of one-loop correlators with the pure-spinor formalism. The first class is described by functions with prescribed monodromies, whose characteristic shuffle-symmetry property leads to a Lie-polynomial structure when multiplied by the local superfields from part I of this series. The second class is given by so-called generalized elliptic integrands (GEIs) that are constructed using the same combinatorial patterns of the BRST pseudo-invariant superfields from part I. Both of them lead to compact and combinatorially rich expressions for the correlators in part III. The identities obeyed by the two classes of worldsheet functions exhibit striking parallels with those of the superfield kinematics. We will refer to this phenomenon as a duality between worldsheet functions and kinematics.

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Mafra-Schlotterer2019_Article_TowardsTheN-pointOne-loopSuper - Accepted Manuscript
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Accepted/In Press date: 29 July 2019
e-pub ahead of print date: 20 August 2019
Published date: August 2019
Additional Information: 72 pages, v2: published version
Keywords: Conformal Field Theory, Superstrings and Heterotic Strings

Identifiers

Local EPrints ID: 433745
URI: http://eprints.soton.ac.uk/id/eprint/433745
ISSN: 1126-6708
PURE UUID: baef9083-7cb3-4ebc-a24c-8c034a6ab665
ORCID for Carlos R. Mafra: ORCID iD orcid.org/0000-0001-9842-9654

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Date deposited: 03 Sep 2019 16:30
Last modified: 27 Jan 2020 13:46

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