Abstract
We demonstrate that the four and six-point tree-level amplitudes of \( \mathcal{N} = 6 \) superconformal Chern-Simons theory (ABJM) enjoy OSp(6|4) dual superconformal symmetry if one enlarges the dual superspace to include three additional Grassmann-even coordinates which correspond to an abelian isometry of CP3. The inclusion of these coordinates enables us to match the nontrivial dual superconformal generators with level-one Yangian generators when acting on on-shell amplitudes. We also discuss some implications of dual conformal symmetry for loop-level amplitudes.
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Z. Bern, L.J . Dixon and V.A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev. D 72 (2005) 085001 [hep-th/0505205] [SPIRES].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [SPIRES].
G.P. Korchemsky, J.M. Drummond and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [arXiv:0707.0243] [SPIRES].
A. Brandhuber, P. Heslop and G. Travaglini, MHV amplitudes in N =4 super Yang-Mills and Wilson loops, Nucl. Phys. B 794 (2008) 231 [arXiv:0707.1153] [SPIRES].
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, On planar gluon amplitudes/Wilson loops duality, Nucl. Phys. B 795 (2008) 52 [arXiv:0709.2368] [SPIRES].
J.M. Drummond, J. Henn, V.A. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [hep-th/0607160] [SPIRES].
A. Brandhuber, P. Heslop and G. Travaglini, A note on dual superconformal symmetry of the N =4 super Yang-Mills S-matrix, Phys. Rev. D 78 (2008) 125005 [arXiv:0807.4097] [SPIRES].
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N =4 super-Yang-Mills theory, Nucl. Phys. B 828 (2010) 317 [arXiv:0807.1095] [SPIRES].
L. Dolan, C.R. Nappi and E. Witten, A relation between approaches to integrability in superconformal Yang-Mills theory, JHEP 10 (2003) 017 [hep-th/0308089] [SPIRES].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [SPIRES].
J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N =4 super Yang-Mills theory, JHEP 05 (2009) 046 [arXiv:0902.2987] [SPIRES].
I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS 5 × S 5 superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [SPIRES].
J.A. Minahan and K. Zarembo, The Bethe-ansatz for N =4 super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [SPIRES].
N. Beisert, C. Kristjansen and M. Staudacher, The dilatation operator of N =4 super Yang-Mills theory, Nucl. Phys. B 664 (2003) 131 [hep-th/0303060] [SPIRES].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [SPIRES].
B. Stefanski, jr, Green-Schwarz action for Type IIA strings on AdS 4 × CP 3, Nucl. Phys. B 808 (2009) 80 [arXiv: 0806.4948] [SPIRES].
G. Arutyunov and S. Frolov, Superstrings on AdS 4 × CP 3 as a coset σ-model, JHEP 09 (2008) 129 [arXiv: 0806.4940] [SPIRES].
J.A. Minahan and K. Zarembo, The Bethe ansatz for superconformal Chern-Simons, JHEP 09 (2008) 040 [arXiv:0806.3951] [SPIRES].
D. Bak and S.-J. Rey, Integrable spin chain in superconformal Chern-Simons theory, JHEP 10 (2008) 053 [arXiv:0807.2063] [SPIRES].
B.I. Zwiebel, Two-loop integrability of planar N =6 superconformal Chern-Simons theory, J. Phys. A 42 (2009) 495402 [arXiv:0901.0411] [SPIRES].
J.A. Minahan, W. Schulgin and K. Zarembo, Two loop integrability for Chern-Simons theories with N =6 supersymmetry, JHEP 03 (2009) 057 [arXiv:0901.1142] [SPIRES].
D. Bak, H. Min and S.-J. Rey, Generalized dynamical spin chain and 4-loop integrability in N =6 superconformal Chern-Simons theory, Nucl. Phys. B 827 (2010) 381 [arXiv:0904.4677] [SPIRES].
D. Bak, H. Min and S.-J. Rey, Integrability of N =6 Chern-Simons theory at six loops and beyond, Phys. Rev. D 81 (2010) 126004 [arXiv:0911.0689] [SPIRES].
N. Gromov and P. Vieira, The all loop AdS 4 /CFT 3 Bethe ansatz, JHEP 01 (2009) 016 [arXiv:0807.0777] [SPIRES].
C. Krishnan, AdS 4 /CFT 3 at one loop, JHEP 09 (2008) 092 [arXiv:0807.4561] [SPIRES].
T. McLoughlin and R. Roiban, Spinning strings at one-loop in AdS 4 × P 3, JHEP 12 (2008) 101 [arXiv:0807.3965] [SPIRES].
L.F. Alday, G. Arutyunov and D. Bykov, Semiclassical quantization of spinning strings in AdS 4 × CP 3, JHEP 11 (2008) 089 [arXiv:0807.4400] [SPIRES].
N. Gromov and V. Mikhaylov, Comment on the scaling function in AdS 4 × CP 3, JHEP 04 (2009) 083 [arXi v:0807.4897] [SPIRES].
T. McLoughlin, R. Roiban and A.A. Tseytlin, Quantum spinning strings in AdS 4 × CP 3 : testing the Bethe Ansatz proposal, JHEP 11 (2008) 069 [arXiv:0809.4038] [SPIRES].
M.A. Bandres and A.E. Lipstein, One-loop corrections to type IIA string theory in AdS 4 × CP 3, JHEP 04 (2010) 059 [arXiv:0911.4061] [SPIRES].
A. Agarwal, N. Beisert and T. McLoughlin, Scattering in mass-deformed N >=4 Chern-Simons models, JHEP 06 (2009) 045 [arXiv:0812.3367] [SPIRES].
T. Bargheer, F. Loebbert and C. Meneghelli, Symmetries of tree-level scattering amplitudes in N =6 superconformal Chern-Simons theory, Phys. Rev. D 82 (2010) 045016 [arXiv:1003.6120] [SPIRES].
Y.-t. Huang and A. Lipstein, Amplitudes of 3D and 6D maximal superconformal theories in supertwistor space, JHEP 10 (2010) 007 [arXiv:1004.4735] [SPIRES].
J.M. Henn, J. Plefka and K. Wiegandt, Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory, JHEP 08 (2010) 032 [arXiv:1004.0226] [SPIRES].
N. Berkovits and J. Maldacena, Fermionic T -duality, dual superconformal symmetry and the amplitude/Wilson loop connection, JHEP 09 (2008) 062 [arXiv:0807.3196] [SPIRES].
N. Beisert, R. Ricci, A.A. Tseytlin and M. Wolf, Dual superconformal symmetry from AdS 5 × S 5 superstring integrability, Phys. Rev. D 78 (2008) 126004 [arXiv:0807.3228] [SPIRES].
J.M. Drummond and L. Ferro, Yangians, Grassmannians and T -duality, JHEP 07 (2010) 027 [arXiv:1001.3348] [SPIRES].
I. Adam, A. Dekel and Y. Oz, On integrable backgrounds self-dual under fermionic T -duality, JHEP 04 (2009) 120 [arXiv:0902.3805] [SPIRES].
P.A. Grassi, D. Sorokin and L. Wulff, Simplifying superstring and D-brane actions in AdS 4 × CP 3 superbackground, JHEP 08 (2009) 060 [arXiv:0903.5407] [SPIRES].
J.M. Drummond, J. Henn, V.A. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [hep-th/0607160] [SPIRES].
Z. Bern, M. Czakon, L.J . Dixon, D.A. Kosower and V.A. Smirnov, The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory, Phys. Rev. D 75 (2007) 085010 [hep-th/0610248] [SPIRES].
Z. Bern, J.J.M. Carrasco, H. Johansson and D.A. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops, Phys. Rev. D 76 (2007) 125020 [arXiv:0705.1864] [SPIRES].
M. Hatsuda and W. Siegel, A new holographic limit of AdS 5 × S 5, Phys. Rev. D 67 (2003) 066005 [hep-th/0211184] [SPIRES].
A. Galperin, E. Ivanov, V. Ogievetsky and E. Sokatchev, Conformal invariance in harmonic superspace in Quantum Field T heory and Quantum Statistics. Vol 2, (1986), I.A. Batalin, C.J. Isham and G.A. Vilkovisky eds., Adam Hilger, Bristol U.K., pg. 233 (1985) Class. Quant. Grav. 4 (1987) 1255 JINR-E2-85-363 [SPIRES].
A. Galperin, E. Ivanov, V. Ogievetsky and E. Sokatchev, Harmonic Superspace, Cambridge University Press, Cambridge U.K. (2001), chapter 9.
Z. Bern, L.J . Dixon, D.C. Dunbar and D.A. Kosower, One-loop n-point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [SPIRES].
Z. Bern, L.J . Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [SPIRES].
M.A. Bandres, A.E. Lipstein and J.H. Schwarz, N = 8 superconformal Chern-Simons theories, JHEP 05 (2008) 025 [arXiv:0803.3242] [SPIRES].
W. Chen, G.W. Semenoff and Y.-S. Wu, Two loop analysis of nonAbelian Chern-Simons theory, Phys. Rev. D 46 (1992) 5521 [hep-th/9209005] [SPIRES].
M. Hatsuda, Y.-t. Huang and W. Siegel, First-quantized N =4 Yang-Mills, JHEP 04 (2009) 058 [arXiv:0812.4569] [SPIRES].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [SPIRES].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [SPIRES].
S. Lee, Yangian invariant scattering amplitudes in supersymmetric Chern-Simons theory, Phys. Rev. Lett. 105 (2010) 151603 [arXiv:1007.4772] [SPIRES].
P. Hoxha, R.R. Martinez-Acosta and C.N. Pope, Kaluza-Klein consistency, Killing vectors and Kähler spaces, Class. Quant. Grav. 17 (2000) 4207 [hep-th/0005172] [SPIRES].
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Huang, Yt., Lipstein, A.E. Dual superconformal symmetry of \( \mathcal{N} = 6 \) Chern-Simons theory. J. High Energ. Phys. 2010, 76 (2010). https://doi.org/10.1007/JHEP11(2010)076
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DOI: https://doi.org/10.1007/JHEP11(2010)076