Tetrahedral modular graph functions
Abstract The low-energy expansion of one-loop amplitudes in type II string theory generates a series of world-sheet integrals whose integrands can be represented by world-sheet Feynman diagrams. These integrands are modular invariant and understanding the structure of the action of the modular Lapla...
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Online Access: | http://link.springer.com/article/10.1007/JHEP09(2017)155 |
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doaj-02687a0e354143caa259ff7c91bf14432020-11-24T21:54:54ZengSpringerOpenJournal of High Energy Physics1029-84792017-09-012017913810.1007/JHEP09(2017)155Tetrahedral modular graph functionsAxel Kleinschmidt0Valentin Verschinin1Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)Abstract The low-energy expansion of one-loop amplitudes in type II string theory generates a series of world-sheet integrals whose integrands can be represented by world-sheet Feynman diagrams. These integrands are modular invariant and understanding the structure of the action of the modular Laplacian on them is important for determining their contribution to string scattering amplitudes. In this paper we study a particular infinite family of such integrands associated with three-loop scalar vacuum diagrams of tetrahedral topology and find closed forms for the action of the Laplacian. We analyse the possible eigenvalues and degeneracies of the Laplace operator by group- and representation-theoretic means.http://link.springer.com/article/10.1007/JHEP09(2017)155M-TheorySuperstrings and Heterotic StringsConformal Field Models in String TheorySupersymmetric Effective Theories |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Axel Kleinschmidt Valentin Verschinin |
spellingShingle |
Axel Kleinschmidt Valentin Verschinin Tetrahedral modular graph functions Journal of High Energy Physics M-Theory Superstrings and Heterotic Strings Conformal Field Models in String Theory Supersymmetric Effective Theories |
author_facet |
Axel Kleinschmidt Valentin Verschinin |
author_sort |
Axel Kleinschmidt |
title |
Tetrahedral modular graph functions |
title_short |
Tetrahedral modular graph functions |
title_full |
Tetrahedral modular graph functions |
title_fullStr |
Tetrahedral modular graph functions |
title_full_unstemmed |
Tetrahedral modular graph functions |
title_sort |
tetrahedral modular graph functions |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2017-09-01 |
description |
Abstract The low-energy expansion of one-loop amplitudes in type II string theory generates a series of world-sheet integrals whose integrands can be represented by world-sheet Feynman diagrams. These integrands are modular invariant and understanding the structure of the action of the modular Laplacian on them is important for determining their contribution to string scattering amplitudes. In this paper we study a particular infinite family of such integrands associated with three-loop scalar vacuum diagrams of tetrahedral topology and find closed forms for the action of the Laplacian. We analyse the possible eigenvalues and degeneracies of the Laplace operator by group- and representation-theoretic means. |
topic |
M-Theory Superstrings and Heterotic Strings Conformal Field Models in String Theory Supersymmetric Effective Theories |
url |
http://link.springer.com/article/10.1007/JHEP09(2017)155 |
work_keys_str_mv |
AT axelkleinschmidt tetrahedralmodulargraphfunctions AT valentinverschinin tetrahedralmodulargraphfunctions |
_version_ |
1725864975571877888 |