One-loop open-string integrals from differential equations: all-order α′-expansions at n points
One-loop open-string integrals from differential equations: all-order α′-expansions at n points
We study generating functions of moduli-space integrals at genus one that are expected to form a basis for massless n-point one-loop amplitudes of open superstrings and open bosonic strings. These integrals are shown to satisfy the same type of linear and homogeneous first-order differential equation w.r.t. the modular parameter τ which is known from the A-elliptic Knizhnik-Zamolodchikov-Bernard associator. The expressions for their τ-derivatives take a universal form for the integration cycles in planar and non-planar one-loop open-string amplitudes. These differential equations manifest the uniformly transcendental appearance of iterated integrals over holomorphic Eisenstein series in the low-energy expansion w.r.t. the inverse string tension α′. In fact, we are led to conjectural matrix representations of certain derivations dual to Eisenstein series. Like this, also the α′-expansion of non-planar integrals is manifestly expressible in terms of iterated Eisenstein integrals without referring to twisted elliptic multiple zeta values. The degeneration of the moduli-space integrals at τ → i∞ is expressed in terms of their genus-zero analogues — (n+2)-point Parke-Taylor integrals over disk boundaries. Our results yield a compact formula for α′-expansions of n-point integrals over boundaries of cylinder- or Möbius-strip worldsheets, where any desired order is accessible from elementary operations.
hep-th
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
(2020)
One-loop open-string integrals from differential equations: all-order α′-expansions at n points.
Journal of High Energy Physics, 2020 (3), [7].
(doi:10.1007/JHEP03(2020)007).
Abstract
We study generating functions of moduli-space integrals at genus one that are expected to form a basis for massless n-point one-loop amplitudes of open superstrings and open bosonic strings. These integrals are shown to satisfy the same type of linear and homogeneous first-order differential equation w.r.t. the modular parameter τ which is known from the A-elliptic Knizhnik-Zamolodchikov-Bernard associator. The expressions for their τ-derivatives take a universal form for the integration cycles in planar and non-planar one-loop open-string amplitudes. These differential equations manifest the uniformly transcendental appearance of iterated integrals over holomorphic Eisenstein series in the low-energy expansion w.r.t. the inverse string tension α′. In fact, we are led to conjectural matrix representations of certain derivations dual to Eisenstein series. Like this, also the α′-expansion of non-planar integrals is manifestly expressible in terms of iterated Eisenstein integrals without referring to twisted elliptic multiple zeta values. The degeneration of the moduli-space integrals at τ → i∞ is expressed in terms of their genus-zero analogues — (n+2)-point Parke-Taylor integrals over disk boundaries. Our results yield a compact formula for α′-expansions of n-point integrals over boundaries of cylinder- or Möbius-strip worldsheets, where any desired order is accessible from elementary operations.
Text
1908.10830 (1)
- Accepted Manuscript
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Accepted/In Press date: 9 February 2020
e-pub ahead of print date: 2 March 2020
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hep-th
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Local EPrints ID: 439477
URI: http://eprints.soton.ac.uk/id/eprint/439477
ISSN: 1029-8479
PURE UUID: a81bcf38-4c9e-42b1-998b-f49c84b52d86
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Date deposited: 24 Apr 2020 16:30
Last modified: 17 Mar 2024 03:33
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Oliver Schlotterer
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