All Order $\alpha$′ Expansion of One-Loop Open-String Integrals - INSPIRE

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All Order $\alpha$ ′ Expansion of One-Loop Open-String Integrals

Carlos R. Mafra
(
- Southampton U.
)
,
Oliver Schlotterer
(
- Uppsala U.
)

Aug 26, 2019

6 pages

Published in:

Phys.Rev.Lett. 124 (2020) 10, 101603

Published: Mar 13, 2020

e-Print:

1908.09848 [hep-th]

DOI:

10.1103/PhysRevLett.124.101603

Report number:

UUITP-34/19

View in:

reference search27 citations

Citations per year

Abstract: (APS)

We present a new method to evaluate the α′ expansion of genus-one integrals over open-string punctures and unravel the structure of the elliptic multiple zeta values in its coefficients. This is done by obtaining a simple differential equation of Knizhnik-Zamolodchikov-Bernard-type satisfied by generating functions of such integrals, and solving it via Picard iteration. The initial condition involves the generating functions at the cusp τ→i∞ and can be reduced to genus-zero integrals.

Note:

6 pages, 2 figures

Elementary Particles and Fields
differential equations
boundary condition
string: open

References(56)

Figures(1)

[1]

A. Levin

- Compos.Math. 106 (1997) 267
•
DOI:
- 10.1023/A:1000193320513

[2]

Multiple Elliptic Polylogarithms

e-Print:
- 1110.6917

[3]

B. Enriquez

- Bull.Soc.Math.Fr. 144 (2016) 395

[4]

The elliptic dilogarithm for the sunset graph

Spencer Bloch
(
- Chicago U., Dept. Math.
)
,
Pierre Vanhove
(
- IPhT, Saclay and
- IHES, Bures-sur-Yvette
)

- J.Number Theor. 148 (2015) 328-364
•
e-Print:
- 1309.5865
•
DOI:
- 10.1016/j.jnt.2014.09.032

[4]

A Feynman integral via higher normal functions

Spencer Bloch
(
- Chicago U., Dept. Math.
)
,
Matt Kerr
(
- Washington U., St. Louis
)
,
Pierre Vanhove
(
- IHES, Bures-sur-Yvette and
- IPhT, Saclay
)

- Compos.Math. 151 (2015) 12, 2329-2375
•
e-Print:
- 1406.2664
•
DOI:
- 10.1112/S0010437X15007472

[4]

Feynman integrals and iterated integrals of modular forms

Luise Adams
(
- Mainz U., Inst. Phys. and
- U. Mainz, PRISMA
)
,
Stefan Weinzierl
(
- Mainz U., Inst. Phys. and
- U. Mainz, PRISMA
)

- Commun.Num.Theor.Phys. 12 (2018) 193-251
•
e-Print:
- 1704.08895
•
DOI:
- 10.4310/CNTP.2018.v12.n2.a1

[4]

Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams

et al.

- J.Math.Phys. 59 (2018) 6, 062305
•
e-Print:
- 1706.01299
•
DOI:
- 10.1063/1.4986417

[4]

An Elliptic Generalization of Multiple Polylogarithms

Ettore Remiddi
(
- Bologna U. and
- INFN, Bologna
)
,
Lorenzo Tancredi
(
- KIT, Karlsruhe, TTP
)

- Nucl.Phys.B 925 (2017) 212-251
•
e-Print:
- 1709.03622
•
DOI:
- 10.1016/j.nuclphysb.2017.10.007

[4]

Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms

Jacob L. Bourjaily
(
- Bohr Inst.
)
,
Andrew J. McLeod
(
- Bohr Inst.
)
,
Marcus Spradlin
(
- Princeton, Inst. Advanced Study and
- Brown U.
)
,
Matt von Hippel
(
- Bohr Inst.
)
,
Matthias Wilhelm
(
- Bohr Inst.
)

- Phys.Rev.Lett. 120 (2018) 12, 121603
•
e-Print:
- 1712.02785
•
DOI:
- 10.1103/PhysRevLett.120.121603

[4]

Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

Johannes Broedel
(
- Humboldt U., Berlin, Inst. Math. and
- Humboldt U., Berlin
)
,
Claude Duhr
(
- CERN and
- Louvain U., CP3
)
,
Falko Dulat
(
- SLAC
)
,
Lorenzo Tancredi
(
- CERN
)

- JHEP 05 (2018) 093
•
e-Print:
- 1712.07089
•
DOI:
- 10.1007/JHEP05(2018)093

[4]

Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral

Johannes Broedel
(
- Humboldt U., Berlin, Inst. Math. and
- Humboldt U., Berlin
)
,
Claude Duhr
(
- CERN and
- Louvain U., CP3
)
,
Falko Dulat
(
- SLAC
)
,
Lorenzo Tancredi
(
- CERN
)

- Phys.Rev.D 97 (2018) 11, 116009
•
e-Print:
- 1712.07095
•
DOI:
- 10.1103/PhysRevD.97.116009

[4]

Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series

Johannes Broedel
(
- Humboldt U., Berlin
)
,
Claude Duhr
(
- CERN and
- Louvain U., CP3
)
,
Falko Dulat
(
- SLAC
)
,
Brenda Penante
(
- CERN
)
,
Lorenzo Tancredi
(
- CERN
)

- JHEP 08 (2018) 014
•
e-Print:
- 1803.10256
•
DOI:
- 10.1007/JHEP08(2018)014

[4]

Planar Double Box Integral for Top Pair Production with a Closed Top Loop to all orders in the Dimensional Regularization Parameter

Luise Adams
(
- Mainz U., Inst. Phys. and
- U. Mainz, PRISMA
)
,
Ekta Chaubey
(
- Mainz U., Inst. Phys. and
- U. Mainz, PRISMA
)
,
Stefan Weinzierl
(
- Mainz U., Inst. Phys. and
- U. Mainz, PRISMA
)

- Phys.Rev.Lett. 121 (2018) 14, 142001
•
e-Print:
- 1804.11144
•
DOI:
- 10.1103/PhysRevLett.121.142001

[4]

Analytic results for the planar double box integral relevant to top-pair production with a closed top loop

Luise Adams
(
- Mainz U., Inst. Phys. and
- U. Mainz, PRISMA
)
,
Ekta Chaubey
(
- Mainz U., Inst. Phys. and
- U. Mainz, PRISMA
)
,
Stefan Weinzierl
(
- Mainz U., Inst. Phys. and
- U. Mainz, PRISMA
)

- JHEP 10 (2018) 206
•
e-Print:
- 1806.04981
•
DOI:
- 10.1007/JHEP10(2018)206

[4]

KMPB Conference: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory

J. Broedel
,
C. Duhr
,
F. Dulat
,
B. Penante
,
L. Tancredi

[4]

The $\rho$ parameter at three loops and elliptic integrals

et al.

- PoS LL2018 (2018) 017
•
e-Print:
- 1807.05287
•
DOI:
- 10.22323/1.303.0017

[4]

Elliptic polylogarithms and Feynman parameter integrals

Johannes Broedel
(
- Humboldt U., Berlin, Inst. Math.
)
,
Claude Duhr
(
- CERN and
- Louvain U., CP3
)
,
Falko Dulat
(
- SLAC
)
,
Brenda Penante
(
- CERN
)
,
Lorenzo Tancredi
(
- CERN
)

- JHEP 05 (2019) 120
•
e-Print:
- 1902.09971
•
DOI:
- 10.1007/JHEP05(2019)120

[4]

The unequal mass sunrise integral expressed through iterated integrals on $\overline{\mathcal M}_{1,3}$

Christian Bogner
(
- Mainz U., Inst. Phys.
)
,
Stefan Müller-Stach
(
- Mainz U.
)
,
Stefan Weinzierl
(
- Mainz U., Inst. Phys.
)

- Nucl.Phys.B 954 (2020) 114991
•
e-Print:
- 1907.01251
•
DOI:
- 10.1016/j.nuclphysb.2020.114991

[4]

An analytic solution for the equal-mass banana graph

Johannes Broedel
(
- Humboldt U., Berlin
)
,
Claude Duhr
(
- CERN and
- Louvain U., CP3
)
,
Falko Dulat
(
- SLAC
)
,
Robin Marzucca
(
- Louvain U., CP3
)
,
Brenda Penante
(
- CERN
)

et al.

- JHEP 09 (2019) 112
•
e-Print:
- 1907.03787
•
DOI:
- 10.1007/JHEP09(2019)112

[5]

The $\varepsilon$ -form of the differential equations for Feynman integrals in the elliptic case

Luise Adams
(
- U. Mainz, PRISMA
)
,
Stefan Weinzierl
(
- U. Mainz, PRISMA
)

- Phys.Lett.B 781 (2018) 270-278
•
e-Print:
- 1802.05020
•
DOI:
- 10.1016/j.physletb.2018.04.002

[6]

Elliptic multiple zeta values and one-loop superstring amplitudes

Johannes Broedel
(
- Zurich, ETH
)
,
Carlos R. Mafra
(
- Cambridge U., DAMTP
)
,
Nils Matthes
(
- Hamburg U., Dept. Math.
)
,
Oliver Schlotterer
(
- Potsdam, Max Planck Inst.
)

- JHEP 07 (2015) 112
•
e-Print:
- 1412.5535
•
DOI:
- 10.1007/JHEP07(2015)112

[7]

Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes

- J.Phys.A 51 (2018) 28, 285401
•
e-Print:
- 1704.03449
•
DOI:
- 10.1088/1751-8121/aac601

[8]

Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory

J. Blümlein
,
C. Schneider
,
P. Paule
,
J. Broedel
,
O. Schlotterer

[9]

Relations between elliptic multiple zeta values and a special derivation algebra

- J.Phys.A 49 (2016) 15, 155203
•
e-Print:
- 1507.02254
•
DOI:
- 10.1088/1751-8113/49/15/155203

[10]

Algebra, Arithmetic, and Geometry: in Honor of Yu.I.Manin.Vol. I, Vol.269 of Prog.Math.

D. Calaque
,
B. Enriquez
,
P. Etingof

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