The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM - INSPIRE

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The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM

Lance J. Dixon
(
- CERN and
- SLAC
)
,
James M. Drummond
(
- CERN and
- Annecy, LAPTH
)
,
Johannes M. Henn
(
- Humboldt U., Berlin
)

Apr, 2011

18 pages

Published in:

JHEP 06 (2011) 100

e-Print:

1104.2787 [hep-th]

DOI:

10.1007/JHEP06(2011)100

Report number:

HU-EP-11-17,
CERN-PH-TH-2011-075,
SLAC-PUB-14434,
LAPTH-013-11,
CERN--PH--TH-2011-075,
SLAC--PUB--14434

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Abstract: (arXiv)

We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral

\tilde\Phi_6

with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar

\\mathcal{N}=4

super-Yang-Mills theory,

\Omega^{(1)}

and

\Omega^{(2)}

. The derivative of

\Omega^{(2)}

with respect to one of the conformal invariants yields

\tilde\Phi_6

, while another first-order differential operator applied to

\tilde\Phi_6

yields

\Omega^{(1)}

. We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in

\\mathcal{N}=4

super-Yang-Mills.

Note:

18 pages, 2 figures

Supersymmetric gauge theory
Conformal and W Symmetry
Field Theories in Higher Dimensions
loop integral: 6
dimension: 6
supersymmetry: 4
operator: differential
invariance: conformal
differential equations
Yang-Mills

References(40)

Figures(2)

Magic identities for conformal four-point integrals

- JHEP 01 (2007) 064
•
e-Print:
- hep-th/0607160
•
DOI:
- 10.1088/1126-6708/2007/01/064

The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory

Zvi Bern
(
- UCLA
)
,
Michael Czakon
(
- Wurzburg U. and
- Silesia U.
)
,
Lance J. Dixon
(
- SLAC
)
,
David A. Kosower
(
- Saclay, SPhT
)
,
Vladimir A. Smirnov
(
- Moscow State U.
)

- Phys.Rev.D 75 (2007) 085010
•
e-Print:
- hep-th/0610248
•
DOI:
- 10.1103/PhysRevD.75.085010

On planar gluon amplitudes/Wilson loops duality

- Nucl.Phys.B 795 (2008) 52-68
•
e-Print:
- 0709.2368
•
DOI:
- 10.1016/j.nuclphysb.2007.11.007

Gluon scattering amplitudes at strong coupling

- JHEP 06 (2007) 064
•
e-Print:
- 0705.0303
•
DOI:
- 10.1088/1126-6708/2007/06/064

Conformal properties of four-gluon planar amplitudes and Wilson loops

- Nucl.Phys.B 795 (2008) 385-408
•
e-Print:
- 0707.0243
•
DOI:
- 10.1016/j.nuclphysb.2007.11.041

MHV amplitudes in N=4 super Yang-Mills and Wilson loops

- Nucl.Phys.B 794 (2008) 231-243
•
e-Print:
- 0707.1153
•
DOI:
- 10.1016/j.nuclphysb.2007.11.002

The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space

- JHEP 12 (2010) 018
•
e-Print:
- 1009.2225
•
DOI:
- 10.1007/JHEP12(2010)018

Notes on the scattering amplitude / Wilson loop duality

Simon Caron-Huot
(
- Princeton, Inst. Advanced Study
)

- JHEP 07 (2011) 058
•
e-Print:
- 1010.1167
•
DOI:
- 10.1007/JHEP07(2011)058

Are scattering amplitudes dual to super Wilson loops?

A.V. Belitsky
(
- Arizona State U.
)
,
G.P. Korchemsky
(
- Saclay, SPhT
)
,
E. Sokatchev
(
- CERN and
- IUF, Paris and
- Annecy, LAPTH
)

- Nucl.Phys.B 855 (2012) 333-360
•
e-Print:
- 1103.3008
•
DOI:
- 10.1016/j.nuclphysb.2011.10.014

Pulling the straps of polygons

- JHEP 12 (2011) 011
•
e-Print:
- 1102.0062
•
DOI:
- 10.1007/JHEP12(2011)011

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes

- Nucl.Phys.B 826 (2010) 337-364
•
e-Print:
- 0712.1223
•
DOI:
- 10.1016/j.nuclphysb.2009.10.013

Planar amplitudes in maximally supersymmetric Yang-Mills theory

- Phys.Rev.Lett. 91 (2003) 251602
•
e-Print:
- hep-th/0309040
•
DOI:
- 10.1103/PhysRevLett.91.251602

Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond

Zvi Bern
(
- UCLA
)
,
Lance J. Dixon
(
- SLAC
)
,
Vladimir A. Smirnov
(
- Moscow State U.
)

- Phys.Rev.D 72 (2005) 085001
•
e-Print:
- hep-th/0505205
•
DOI:
- 10.1103/PhysRevD.72.085001

Iterative structure within the five-particle two-loop amplitude

- Phys.Rev.D 74 (2006) 045020
•
e-Print:
- hep-th/0602228
•
DOI:
- 10.1103/PhysRevD.74.045020

Two-loop iteration of five-point N=4 super-Yang-Mills amplitudes

Z. Bern
(
- UCLA
)
,
M. Czakon
(
- Wurzburg U. and
- Silesia U.
)
,
D.A. Kosower
(
- Saclay, SPhT
)
,
R. Roiban
(
- Penn State U.
)
,
V.A. Smirnov
(
- Moscow, INR
)

- Phys.Rev.Lett. 97 (2006) 181601
•
e-Print:
- hep-th/0604074
•
DOI:
- 10.1103/PhysRevLett.97.181601

The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory

et al.

- Phys.Rev.D 78 (2008) 045007
•
e-Print:
- 0803.1465
•
DOI:
- 10.1103/PhysRevD.78.045007

Leading Singularities of the Two-Loop Six-Particle MHV Amplitude

Freddy Cachazo
(
- Perimeter Inst. Theor. Phys.
)
,
Marcus Spradlin
(
- Brown U.
)
,
Anastasia Volovich
(
- Brown U.
)

- Phys.Rev.D 78 (2008) 105022
•
e-Print:
- 0805.4832
•
DOI:
- 10.1103/PhysRevD.78.105022

Three-Loop Leading Singularities and BDS Ansatz for Five Particles

- Phys.Rev.D 78 (2008) 085025
•
e-Print:
- 0808.1054
•
DOI:
- 10.1103/PhysRevD.78.085025

More loops and legs in Higgs-regulated N=4 SYM amplitudes

Johannes M. Henn
(
- Humboldt U., Berlin
)
,
Stephen G. Naculich
(
- Bowdoin Coll.
)
,
Howard J. Schnitzer
(
- Brandeis U.
)
,
Marcus Spradlin
(
- Brown U.
)

- JHEP 08 (2010) 002
•
e-Print:
- 1004.5381
•
DOI:
- 10.1007/JHEP08(2010)002

Hexagon Wilson loop = six-gluon MHV amplitude

- Nucl.Phys.B 815 (2009) 142-173
•
e-Print:
- 0803.1466
•
DOI:
- 10.1016/j.nuclphysb.2009.02.015

Maximally supersymmetric planar Yang-Mills amplitudes at five loops

Z. Bern
(
- UCLA
)
,
J.J.M. Carrasco
(
- UCLA
)
,
Henrik Johansson
(
- UCLA
)
,
D.A. Kosower
(
- Saclay, SPhT and
- Zurich U.
)

- Phys.Rev.D 76 (2007) 125020
•
e-Print:
- 0705.1864
•
DOI:
- 10.1103/PhysRevD.76.125020

Scattering amplitudes on the Coulomb branch of N=4 super Yang-Mills

Johannes M. Henn
(
- Humboldt U., Berlin
)

- Nucl.Phys.B Proc.Suppl. 205-206 (2010) 193-198
•
e-Print:
- 1005.2902
•
DOI:
- 10.1016/j.nuclphysbps.2010.08.042

Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes

Tristan Dennen
(
- UCLA
)
,
Yu-tin Huang
(
- UCLA
)

- JHEP 01 (2011) 140
•
e-Print:
- 1010.5874
•
DOI:
- 10.1007/JHEP01(2011)140

Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions

- JHEP 08 (2011) 014
•
e-Print:
- 1010.5487
•
DOI:
- 10.1007/JHEP08(2011)014

Dual conformal symmetry at loop level: massive regularization

Johannes M. Henn
(
- Humboldt U., Berlin
)

- J.Phys.A 44 (2011) 454011
•
e-Print:
- 1103.1016
•
DOI:
- 10.1088/1751-8113/44/45/454011

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