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Generating series o...
Generating series of all modular graph forms from iterated Eisenstein integrals
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- Gerken, Jan E. (author)
- Albert Einstein Inst, Max Planck Inst Gravitationsphys, DE-14476 Potsdam, Germany.
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- Kleinschmidt, Axel (author)
- Albert Einstein Inst, Max Planck Inst Gravitationsphys, DE-14476 Potsdam, Germany.;Int Solvay Inst ULB, Campus Plaine CP231, BE-1050 Brussels, Belgium.
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- Schlotterer, Oliver (author)
- Uppsala universitet,Teoretisk fysik
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Albert Einstein Inst, Max Planck Inst Gravitationsphys, DE-14476 Potsdam, Germany Albert Einstein Inst, Max Planck Inst Gravitationsphys, DE-14476 Potsdam, Germany.;Int Solvay Inst ULB, Campus Plaine CP231, BE-1050 Brussels, Belgium. (creator_code:org_t)
- Springer Nature, 2020
- 2020
- English.
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In: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; 2020:7
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Abstract
Subject headings
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- We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes. By analysing the differential equation of the generating series we construct a solution for their low-energy expansion to all orders in the inverse string tension alpha '. Our solution is expressed through initial data involving multiple zeta values and certain real-analytic functions of the modular parameter of the torus. These functions are built from real and imaginary parts of holomorphic iterated Eisenstein integrals and should be closely related to Brown's recent construction of real-analytic modular forms. We study the properties of our real-analytic objects in detail and give explicit examples to a fixed order in the alpha ' -expansion. In particular, our solution allows for a counting of linearly independent modular graph forms at a given weight, confirming previous partial results and giving predictions for higher, hitherto unexplored weights. It also sheds new light on the topic of uniform transcendentality of the alpha ' -expansion.
Subject headings
- NATURVETENSKAP -- Fysik -- Subatomär fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences -- Subatomic Physics (hsv//eng)
Keyword
- Conformal Field Models in String Theory
- Scattering Amplitudes
- Superstrings and Heterotic Strings
Publication and Content Type
- ref (subject category)
- art (subject category)
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