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The SFB 676 has been funded by the DFG from 2006 to 2018. The project was completed with a special colloquium in June 2018. A book with the scientific results of the SFB 676 has been published in September 2018.

J. Haller and M. Grefe (eds.), “Particles, Strings and the Early Universe: The Structure of Matter and Space-Time,” Hamburg (2018), DOI: 10.3204/PUBDB-2018-00782.

Many research directions developed within the SFB 676 will be continued within the Cluster of Excellence "Quantum Universe" starting 1 January 2019.

A9 – Loops and Legs

Project Leaders

Bernd Kniehl (e-mail | group homepage)

Rutger Boels (e-mail | group homepage)


In order to fully exploit the physics potential of the CERN Large Hadron Collider, theoretical predictions must be pushed to a higher level of accuracy. Driven by experimental demands, the ability to calculate massless-particle scattering amplitudes in particular has made quantum leaps in recent years, revealing many tantalizing structures. This project makes use of the natural synergy in this area between directly experimentally relevant calculations and theoretically motivated considerations to develop the new technology toward maturity.


Gustavo Alvarez Cosque

Mikhail Kalmykov

Oleg Tarasov

Oleg Veretin

Former members

Isabella Bierenbaum

Paolo Bolzoni

Tobias Hansen

Christoph Horst

Reinke Isermann

Arthur Lipstein

Hui Luo

Gang Yang


Get these publications as bibtex-file

"Functional reduction of Feynman integrals"
Tarasov, O. V.
JHEP 02, 173 (2019)
doi: 10.1007/JHEP02(2019)173
eprint: 1901.09442 [hep-ph]

"The Sudakov form factor at four loops in maximal super Yang-Mills theory"
Boels, Rutger H. and Huber, Tobias and Yang, Gang
JHEP 01, 153 (2018)
doi: 10.1007/JHEP01(2018)153
eprint: 1711.08449 [hep-th]

"A minimal approach to the scattering of physical massless bosons"
Boels, Rutger H. and Luo, Hui
JHEP 05, 063 (2018)
doi: 10.1007/JHEP05(2018)063
eprint: 1710.10208 [hep-th]

"Three-loop massive tadpoles and polylogarithms through weight six"
Kniehl, B. A. and Pikelner, A. F. and Veretin, O. L.
JHEP 08, 024 (2017)
doi: 10.1007/JHEP08(2017)024
eprint: 1705.05136 [hep-ph]

"Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory"
Boels, Rutger H. and Huber, Tobias and Yang, Gang
Phys. Rev. Lett. 119, 201601 (2017)
doi: 10.1103/PhysRevLett.119.201601
eprint: 1705.03444 [hep-th]

"Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation"
Kalmykov, Mikhail Yu. and Kniehl, Bernd A.
JHEP 07, 031 (2017)
doi: 10.1007/JHEP07(2017)031
eprint: 1612.06637 [hep-th]

"Explicit calculation of multi-fold contour integrals of certain ratios of Euler gamma functions. Part 1"
Gonzalez, Ivan and Kniehl, Bernd A. and Kondrashuk, Igor and Notte-Cuello, Eduardo A. and Parra-Ferrada, Ivan and Rojas-Medar, Marko A.
Nucl. Phys. B925, 607-614 (2017)
doi: 10.1016/j.nuclphysb.2017.06.027
eprint: 1608.04148 [math.MP]

"Graviton and gluon scattering from first principles"
Boels, Rutger H. and Medina, Ricardo
Phys. Rev. Lett. 118, 061602 (2017)
doi: 10.1103/PhysRevLett.118.061602
eprint: 1607.08246 [hep-th]

"HYPERDIRE—HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Lauricella function Fc of three variables"
Bytev, Vladimir V. and Kniehl, Bernd A.
Comput. Phys. Commun. 206, 78-83 (2016)
doi: 10.1016/j.cpc.2016.04.016
eprint: 1602.00917 [math-ph]

"Perturbative quantum gravity in double field theory"
Boels, Rutger H. and Horst, Christoph
JHEP 04, 120 (2016)
doi: 10.1007/JHEP04(2016)120
eprint: 1512.03192 [hep-th]

"Master integrals for the four-loop Sudakov form factor"
Boels, Rutger and Kniehl, Bernd A. and Yang, Gang
Nucl. Phys. B902, 387-414 (2016)
doi: 10.1016/j.nuclphysb.2015.11.016
eprint: 1508.03717 [hep-th]

"Conformal correlators of mixed-symmetry tensors"
Costa, Miguel S. and Hansen, Tobias
JHEP 1502, 151 (2015)
doi: 10.1007/JHEP02(2015)151
eprint: 1411.7351 [hep-th]

"String theory in target space"
Boels, Rutger H. and Hansen, Tobias
JHEP 1406, 054 (2014)
doi: 10.1007/JHEP06(2014)054
eprint: 1402.6356 [hep-th]

"On the field theory expansion of superstring five point amplitudes"
Boels, Rutger H.
Nucl.Phys. B876, 215-233 (2013)
doi: 10.1016/j.nuclphysb.2013.08.009
eprint: 1304.7918 [hep-th]

"Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions"
Kniehl, Bernd and Kondrashuk, Igor and Notte-Cuello, Eduardo A. and Ferrada, Ivan Parra and Rojas-Medar, Marko
Nucl.Phys. B876, 322-333 (2013)
doi: 10.1016/j.nuclphysb.2013.08.002
eprint: 1304.3004 [hep-th]

"Colour-Kinematics Duality for One-Loop Rational Amplitudes"
Boels, Rutger H. and Isermann, Reinke Sven and Monteiro, Ricardo and O'Connell, Donal
JHEP 1304, 107 (2013)
doi: 10.1007/JHEP04(2013)107
eprint: 1301.4165 [hep-th]

"On powercounting in perturbative quantum gravity theories through color-kinematic duality"
Boels, Rutger H. and Isermann, Reinke Sven
JHEP 1306, 017 (2013)
doi: 10.1007/JHEP06(2013)017
eprint: 1212.3473

"Color-kinematic Duality for Form Factors"
Boels, Rutger H. and Kniehl, Bernd A. and Tarasov, Oleg V. and Yang, Gang
JHEP 1302, 063 (2013)
doi: 10.1007/JHEP02(2013)063
eprint: 1211.7028 [hep-th]

"Tree-loop duality relation beyond simple poles"
Bierenbaum, Isabella and Buchta, Sebastian and Draggiotis, Petros and Malamos, Ioannis and Rodrigo, German
JHEP 1303, 025 (2013)
doi: 10.1007/JHEP03(2013)025
eprint: 1211.5048 [hep-ph]

"Solution to Bethe-Salpeter equation via Mellin-Barnes transform"
Allendes, Pedro and Kniehl, Bernd and Kondrashuk, Igor and Cuello, Eduardo A. Notte and Medar, Marko Rojas
Nucl.Phys. B870, 243-277 (2013)
doi: 10.1016/j.nuclphysb.2013.01.012
eprint: 1205.6257 [hep-th]

"When epsilon expansion of hypergeometric functions is expressible in terms of multiple polylogarithms: the two-variable examples"
Bytev, Vladimir V. and Kalmykov, Mikhail Yu. and Kniehl, Bernd A.
PoS LL2012, 029 (2012)
eprint: 1212.4719 [hep-th]

"Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions"
Kalmykov, Mikhail Yu. and Kniehl, Bernd A.
Phys.Lett. B714, 103-109 (2012)
doi: 10.1016/j.physletb.2012.06.045
eprint: 1205.1697 [hep-th]

"Maximal R-symmetry violating amplitudes in type IIB superstring theory"
Boels, Rutger H.
Phys.Rev.Lett. 109, 081602 (2012)
doi: 10.1103/PhysRevLett.109.081602
eprint: 1204.4208 [hep-th]

"Counting master integrals: integration-by-parts procedure with effective mass"
Kniehl, Bernd A. and Kotikov, Anatoly V.
Phys.Lett. B712, 233-234 (2012)
doi: 10.1016/j.physletb.2012.04.071
eprint: 1202.2242 [hep-ph]

"Analytic two-loop form factors in \mathcalN=4 SYM"
Brandhuber, Andreas and Travaglini, Gabriele and Yang, Gang
JHEP 1205, 082 (2012)
doi: 10.1007/JHEP05(2012)082
eprint: 1201.4170 [hep-th]

"Three particle superstring amplitudes with massive legs"
Boels, Rutger H.
JHEP 1206, 026 (2012)
doi: 10.1007/JHEP06(2012)026
eprint: 1201.2655 [hep-th]

"Simple superamplitudes in higher dimensions"
Boels, Rutger H. and O'Connell, Donal
JHEP 1206, 163 (2012)
doi: 10.1007/JHEP06(2012)163
eprint: 1201.2653 [hep-th]

"Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts"
Boels, Rutger H. and Isermann, Reinke Sven
JHEP 1203, 051 (2012)
doi: 10.1007/JHEP03(2012)051
eprint: 1110.4462 [hep-th]

"New relations for scattering amplitudes in Yang-Mills theory at loop level"
Boels, Rutger H. and Isermann, Reinke Sven
Phys.Rev. D85, 021701 (2012)
doi: 10.1103/PhysRevD.85.021701
eprint: 1109.5888 [hep-th]

"Finding new relationships between hypergeometric functions by evaluating Feynman integrals"
Kniehl, Bernd A. and Tarasov, Oleg V.
Nucl.Phys. B854, 841-852 (2012)
doi: 10.1016/j.nuclphysb.2011.09.015
eprint: 1108.6019 [math-ph]

"The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction"
Yost, S.A. and Bytev, V.V. and Kalmykov, M. Yu. and Kniehl, B.A. and Ward, B.F.L.
eprint: 1110.0210 [math-ph]

"Counting master integrals: Integration by parts versus differential reduction"
Kalmykov, Mikhail Yu. and Kniehl, Bernd A.
Phys.Lett. B702, 268-271 (2011)
doi: 10.1016/j.physletb.2011.06.094
eprint: 1105.5319 [math-ph]

"HYPERDIRE, HYPERgeometric functions DIfferential REduction: MATHEMATICA-based packages for differential reduction of generalized hypergeometric functions pFp-1, F1, F2, F3, F4"
Bytev, Vladimir V. and Kalmykov, Mikhail Yu. and Kniehl, Bernd A.
Comput.Phys.Commun. 184, 2332-2342 (2011)
doi: 10.1016/j.cpc.2013.05.009
eprint: 1105.3565 [math-ph]

"On-shell supersymmetry for massive multiplets"
Boels, Rutger H. and Schwinn, Christian
Phys.Rev. D84, 065006 (2011)
doi: 10.1103/PhysRevD.84.065006
eprint: 1104.2280 [hep-th]

"Differential Reduction Techniques for the Evaluation of Feynman Diagrams"
Yost, S.A. and Bytev, V.V. and Kalmykov, M. Yu. and Kniehl, B.A. and Ward, B.F.L.
PoS ICHEP2010, 135 (2010)
eprint: 1101.2348 [math-ph]

"On BCFW shifts of integrands and integrals"
Boels, Rutger H.
JHEP 1011, 113 (2010)
doi: 10.1007/JHEP11(2010)113
eprint: 1008.3101 [hep-th]

"'Sixth root of unity' and Feynman diagrams: Hypergeometric function approach point of view"
Kalmykov, Mikhail Yu. and Kniehl, Bernd A.
Nucl.Phys.Proc.Suppl. 205-206, 129-134 (2010)
doi: 10.1016/j.nuclphysbps.2010.08.031
eprint: 1007.2373 [math-ph]


Master thesis: "Three point scattering amplitudes in string theory"
Kalamakis, Georgios
Universität Hamburg (2013)

Master thesis: "Relations among color-ordered gauge theory scattering amplitudes at higher loop-order"
Reichenbächer, Thomas
Universität Hamburg (2013)

PhD thesis: "Dissecting CFT Correlators and String Amplitudes: Conformal Blocks and On-Shell Recursion for General Tensor Fields"
Hansen, Tobias
Universität Hamburg (2015)
doi: 10.3204/DESY-THESIS-2015-026
[ link ]

PhD thesis: "Of Gluons and Gravitons: Exploring Color-Kinematics Duality"
Isermann, Reinke Sven
Universität Hamburg (2013)
[ link ]

Impressum  | last modified 27 Aug 2019