Abstract
To explore color/kinematics duality for general representations of the gauge group we formulate the duality for general abelian orbifolds of the SU(N), \( \mathcal{N} \) = 4 super Yang-Mills theory in four dimensions, which have fields in the bi-fundamental representation, and use it to construct explicitly complete four-vector and four-scalar amplitudes at one loop. For fixed number of supercharges, graph-organized L-loop n-point integrands of all orbifold theories are given in terms of a fixed set of polynomials labeled by L representations of the orbifold group. In contrast to the standard duality-satisfying presentation of amplitudes of the \( \mathcal{N} \) = 4 super Yang-Mills theory, each graph may appear several times with different internal states. The color and R-charge flow provide a way to deform the amplitudes of orbifold theories to those of more general quiver gauge theories which do not necessarily exhibit color/kinematics duality on their own.
Based on the organization of amplitudes required by the duality between color and kinematics in orbifold theories we show how the amplitudes of certain non-factorized mattercoupled supergravity theories can be found through a double-copy construction.
We also carry out a comprehensive search for theories with fields solely in the adjoint representation of the gauge group and amplitudes exhibiting color/kinematics duality for all external states and find an interesting relation between supersymmetry and existence of the duality.
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References
Z. Bern, J. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
J. Drummond, J. Henn, V. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [hep-th/0607160] [INSPIRE].
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] [INSPIRE].
Z. Bern, J. Carrasco, H. Johansson and D. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops, Phys. Rev. D 76 (2007) 125020 [arXiv:0705.1864] [INSPIRE].
L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [INSPIRE].
J. Drummond, G. Korchemsky and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [arXiv:0707.0243] [INSPIRE].
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] [INSPIRE].
B. Eden, G.P. Korchemsky and E. Sokatchev, From correlation functions to scattering amplitudes, JHEP 12 (2011) 002 [arXiv:1007.3246] [INSPIRE].
L.F. Alday, B. Eden, G.P. Korchemsky, J. Maldacena and E. Sokatchev, From correlation functions to Wilson loops, JHEP 09 (2011) 123 [arXiv:1007.3243] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
Y.-t. Huang and H. Johansson, Equivalent D = 3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories, Phys. Rev. Lett. 110 (2013) 171601 [arXiv:1210.2255] [INSPIRE].
Y.-t. Huang, H. Johansson and S. Lee, On Three-Algebra and Bi-Fundamental Matter Amplitudes and Integrability of Supergravity, JHEP 11 (2013) 050 [arXiv:1307.2222] [INSPIRE].
L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on Orbifolds, Nucl. Phys. B 261 (1985) 678 [INSPIRE].
L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on Orbifolds. 2., Nucl. Phys. B 274 (1986) 285 [INSPIRE].
L.J. Dixon, D. Friedan, E.J. Martinec and S.H. Shenker, The Conformal Field Theory of Orbifolds, Nucl. Phys. B 282 (1987) 13 [INSPIRE].
M.R. Douglas and G.W. Moore, D-branes, quivers and ALE instantons, hep-th/9603167 [INSPIRE].
S. Kachru and E. Silverstein, 4 − D conformal theories and strings on orbifolds, Phys. Rev. Lett. 80 (1998) 4855 [hep-th/9802183] [INSPIRE].
A.E. Lawrence, N. Nekrasov and C. Vafa, On conformal field theories in four-dimensions, Nucl. Phys. B 533 (1998) 199 [hep-th/9803015] [INSPIRE].
A. Dymarsky, I. Klebanov and R. Roiban, Perturbative search for fixed lines in large N gauge theories, JHEP 08 (2005) 011 [hep-th/0505099] [INSPIRE].
M. Bershadsky and A. Johansen, Large N limit of orbifold field theories, Nucl. Phys. B 536 (1998) 141 [hep-th/9803249] [INSPIRE].
J.J.M. Carrasco, M. Chiodaroli, M. Günaydin and R. Roiban, One-loop four-point amplitudes in pure and matter-coupled N < = 4 supergravity, JHEP 03 (2013) 056 [arXiv:1212.1146] [INSPIRE].
Z. Bern, S. Davies, T. Dennen, Y.-t. Huang and J. Nohle, Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops, arXiv:1303.6605 [INSPIRE].
H. Johansson and A. Ochirov, to appear.
H. Johansson, Fundamental representation color-kinematics duality and N < 4 supergravity, Seminar in the program Physics and Mathematics of Scattering Amplitudes, at the Simons Center for Geometry and Physics, October 22 2013, http://scgp.stonybrook.edu/archives/9151.
Z. Bern, T. Dennen, Y.-T. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory, Phys. Rev. D 82 (2010) 065003 [arXiv:1004.0693] [INSPIRE].
J. Nohle, Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter, arXiv:1309.7416 [INSPIRE].
E. Fuchs, The U(1)s in the finite N limit of orbifold field theories, JHEP 10 (2000) 028 [hep-th/0003235] [INSPIRE].
A. Dymarsky, I. Klebanov and R. Roiban, Perturbative gauge theory and closed string tachyons, JHEP 11 (2005) 038 [hep-th/0509132] [INSPIRE].
I.R. Klebanov and A.A. Tseytlin, D-branes and dual gauge theories in type 0 strings, Nucl. Phys. B 546 (1999) 155 [hep-th/9811035] [INSPIRE].
S.H. Henry Tye and Y. Zhang, Dual Identities inside the Gluon and the Graviton Scattering Amplitudes, JHEP 06 (2010) 071 [Erratum ibid. 1104 (2011) 114] [arXiv:1003.1732] [INSPIRE].
N. Bjerrum-Bohr, P.H. Damgaard, T. Sondergaard and P. Vanhove, Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes, JHEP 06 (2010) 003 [arXiv:1003.2403] [INSPIRE].
J. Broedel and J.J.M. Carrasco, Virtuous Trees at Five and Six Points for Yang-Mills and Gravity, Phys. Rev. D 84 (2011) 085009 [arXiv:1107.4802] [INSPIRE].
Z. Bern and T. Dennen, A Color Dual Form for Gauge-Theory Amplitudes, Phys. Rev. Lett. 107 (2011) 081601 [arXiv:1103.0312] [INSPIRE].
R. Monteiro and D. O’Connell, The Kinematic Algebra From the Self-Dual Sector, JHEP 07 (2011) 007 [arXiv:1105.2565] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, arXiv:1309.0885 [INSPIRE].
R. Monteiro and D. O’Connell, The Kinematic Algebras from the Scattering Equations, arXiv:1311.1151 [INSPIRE].
M. Kiermaier, Gravity as the square of gauge theory, presented at Amplitudes 2010, http://www.strings.ph.qmul.ac.uk/~theory/Amplitudes2010.
N. Bjerrum-Bohr, P.H. Damgaard, T. Sondergaard and P. Vanhove, The Momentum Kernel of Gauge and Gravity Theories, JHEP 01 (2011) 001 [arXiv:1010.3933] [INSPIRE].
C.R. Mafra, O. Schlotterer and S. Stieberger, Explicit BCJ Numerators from Pure Spinors, JHEP 07 (2011) 092 [arXiv:1104.5224] [INSPIRE].
Z. Bern, J. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, The Complete Four-Loop Four-Point Amplitude in N = 4 super-Yang-Mills Theory, Phys. Rev. D 82 (2010) 125040 [arXiv:1008.3327] [INSPIRE].
J.J. Carrasco and H. Johansson, Five-Point Amplitudes in \( \mathcal{N} \) = 4 super-Yang-Mills Theory and \( \mathcal{N} \) = 8 Supergravity, Phys. Rev. D 85 (2012) 025006 [arXiv:1106.4711] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop selfdual and N = 4 super Yang-Mills, Phys. Lett. B 394 (1997) 105 [hep-th/9611127] [INSPIRE].
N.E.J. Bjerrum-Bohr, T. Dennen, R. Monteiro and D. O’Connell, Integrand Oxidation and One-Loop Colour-Dual Numerators in N = 4 Gauge Theory, JHEP 07 (2013) 092 [arXiv:1303.2913] [INSPIRE].
Y.-J. Du, B. Feng and C.-H. Fu, BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory, JHEP 08 (2011) 129 [arXiv:1105.3503] [INSPIRE].
Z. Bern, J. Carrasco, L. Dixon, H. Johansson and R. Roiban, Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes, Phys. Rev. D 85 (2012) 105014 [arXiv:1201.5366] [INSPIRE].
L. Magnea and G.F. Sterman, Analytic continuation of the Sudakov form-factor in QCD, Phys. Rev. D 42 (1990) 4222 [INSPIRE].
A. Ochirov and P. Tourkine, BCJ duality and double copy in the closed string sector, arXiv:1312.1326 [INSPIRE].
Z. Bern and A. Morgan, Massive loop amplitudes from unitarity, Nucl. Phys. B 467 (1996) 479 [hep-ph/9511336] [INSPIRE].
H. Kawai, D. Lewellen and S. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
Z. Bern, L.J. Dixon, M. Perelstein and J. Rozowsky, Multileg one loop gravity amplitudes from gauge theory, Nucl. Phys. B 546 (1999) 423 [hep-th/9811140] [INSPIRE].
P. Tourkine and P. Vanhove, One-loop four-graviton amplitudes in \( \mathcal{N} \) = 4 supergravity models, Phys. Rev. D 87 (2013) 045001 [arXiv:1208.1255] [INSPIRE].
H. Johansson, A. Sabio Vera, E. Serna Campillo and M.A. Vazquez-Mozo, Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction, JHEP 10 (2013) 215 [arXiv:1307.3106] [INSPIRE].
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Chiodaroli, M., Jin, Q. & Roiban, R. Color/kinematics duality for general abelian orbifolds of \( \mathcal{N} \) = 4 super Yang-Mills theory. J. High Energ. Phys. 2014, 152 (2014). https://doi.org/10.1007/JHEP01(2014)152
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DOI: https://doi.org/10.1007/JHEP01(2014)152