Differential equations for multi-loop integrals and two-dimensional kinematics - INSPIRE

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Differential equations for multi-loop integrals and two-dimensional kinematics

L. Ferro
(
- Humboldt U., Berlin
)

Apr, 2012

25 pages

Published in:

JHEP 04 (2013) 160

e-Print:

1204.1031 [hep-th]

DOI:

10.1007/JHEP04(2013)160

Report number:

HU-EP-12-12

View in:

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Abstract: (Springer)

In this paper we consider multi-loop integrals appearing in MHV scattering amplitudes of planar SYM. Through particular differential operators which reduce the loop order by one, we present explicit equations for the two-loop eight-point finite diagrams which relate them to massive hexagons. After the reduction to two-dimensional kinematics, we solve them using symbol technology. The terms invisible to the symbols are found through boundary conditions coming from double soft limits. These equations are valid at all-loop order for double pentaladders and allow to solve iteratively loop integrals given lower-loop information. Comments are made about multi-leg and multi-loop integrals which can appear in this special kinematics. The main motivation of this investigation is to get a deeper understanding of these tools in this configuration, as well as for their application in general four-dimensional kinematics and to less supersymmetric theories.

Note:

25 pages, 7 figures

gauge field theory: Yang-Mills: supersymmetry
dimension: 2
operator: differential
supersymmetry: 4
dimension: 4
kinematics
differential equations
scattering amplitude
boundary condition
loop integral

References(48)

Figures(17)

[1]

Magic identities for conformal four-point integrals

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

[2]

Gluon scattering amplitudes at strong coupling

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

[3]

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

[4]

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

[5]

Comments on gluon scattering amplitudes via AdS/CFT

- JHEP 11 (2007) 068
•
e-Print:
- 0710.1060
•
DOI:
- 10.1088/1126-6708/2007/11/068

[6]

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

[7]

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

[8]

The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude

- Phys.Lett.B 662 (2008) 456-460
•
e-Print:
- 0712.4138
•
DOI:
- 10.1016/j.physletb.2008.03.032

[9]

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

[10]

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

[11]

Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory

- Nucl.Phys.B 828 (2010) 317-374
•
e-Print:
- 0807.1095
•
DOI:
- 10.1016/j.nuclphysb.2009.11.022

[12]

A Note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix

- Phys.Rev.D 78 (2008) 125005
•
e-Print:
- 0807.4097
•
DOI:
- 10.1103/PhysRevD.78.125005

[13]

Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory

James M. Drummond
(
- Annecy, LAPTH
)
,
Johannes M. Henn
(
- Humboldt U., Berlin
)
,
Jan Plefka
(
- Humboldt U., Berlin
)

- JHEP 05 (2009) 046
•
e-Print:
- 0902.2987
•
DOI:
- 10.1088/1126-6708/2009/05/046

[14]

A Duality For The S Matrix

- JHEP 03 (2010) 020
•
e-Print:
- 0907.5418
•
DOI:
- 10.1007/JHEP03(2010)020

[15]

Dual Superconformal Invariance, Momentum Twistors and Grassmannians

- JHEP 11 (2009) 045
•
e-Print:
- 0909.0250
•
DOI:
- 10.1088/1126-6708/2009/11/045

[16]

The Yangian origin of the Grassmannian integral

J.M. Drummond
(
- Annecy, LAPTH
)
,
L. Ferro
(
- Annecy, LAPTH
)

- JHEP 12 (2010) 010
•
e-Print:
- 1002.4622
•
DOI:
- 10.1007/JHEP12(2010)010

[17]

Superconformal invariants for scattering amplitudes in N=4 SYM theory

G.P. Korchemsky
(
- Saclay, SPhT
)
,
E. Sokatchev
(
- Annecy, LAPTH
)

- Nucl.Phys.B 839 (2010) 377-419
•
e-Print:
- 1002.4625
•
DOI:
- 10.1016/j.nuclphysb.2010.05.022

[18]

New differential equations for on-shell loop integrals

James M. Drummond
(
- CERN and
- Annecy, LAPTH
)
,
Johannes M. Henn
(
- Humboldt U., Berlin
)
,
Jaroslav Trnka
(
- Princeton, Inst. Advanced Study and
- Princeton U.
)

- JHEP 04 (2011) 083
•
e-Print:
- 1010.3679
•
DOI:
- 10.1007/JHEP04(2011)083

[19]

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
)

- JHEP 06 (2011) 100
•
e-Print:
- 1104.2787
•
DOI:
- 10.1007/JHEP06(2011)100

[20]

The one-loop six-dimensional hexagon integral with three massive corners

Vittorio Del Duca
(
- Unlisted, IT and
- KIPAC, Menlo Park
)
,
Lance J. Dixon
(
- SLAC and
- CERN
)
,
James M. Drummond
(
- CERN and
- Annecy, LAPTH
)
,
Claude Duhr
(
- Durham U., IPPP and
- KIPAC, Menlo Park
)
,
Johannes M. Henn
(
- Humboldt U., Berlin and
- KIPAC, Menlo Park
)

et al.

- Phys.Rev.D 84 (2011) 045017
•
e-Print:
- 1105.2011
•
DOI:
- 10.1103/PhysRevD.84.045017

[21]

The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM

- JHEP 01 (2011) 041
•
e-Print:
- 1008.2958
•
DOI:
- 10.1007/JHEP01(2011)041

[22]

Local Integrals for Planar Scattering Amplitudes

- JHEP 06 (2012) 125
•
e-Print:
- 1012.6032
•
DOI:
- 10.1007/JHEP06(2012)125

[23]

Eliminating spurious poles from gauge-theoretic amplitudes

Andrew Hodges
(
- Oxford U.
)

- JHEP 05 (2013) 135
•
e-Print:
- 0905.1473
•
DOI:
- 10.1007/JHEP05(2013)135

[24]

The Two-Loop Hexagon Wilson Loop in N = 4 SYM

Vittorio Del Duca
(
- CERN and
- Frascati
)
,
Claude Duhr
(
- Durham U., IPPP
)
,
Vladimir A. Smirnov
(
- Moscow State U. and
- SINP, Moscow
)

- JHEP 05 (2010) 084
•
e-Print:
- 1003.1702
•
DOI:
- 10.1007/JHEP05(2010)084

[25]

A Two-Loop Octagon Wilson Loop in N = 4 SYM

Vittorio Del Duca
(
- CERN and
- Frascati
)
,
Claude Duhr
(
- Durham U., IPPP
)
,
Vladimir A. Smirnov
(
- SINP, Moscow
)

- JHEP 09 (2010) 015
•
e-Print:
- 1006.4127
•
DOI:
- 10.1007/JHEP09(2010)015

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