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Conformal anomaly of super Wilson loop. (English) Zbl 1246.81105
Summary: Classically supersymmetric Wilson loop on a null polygonal contour possesses all symmetries required to match it onto non-MHV amplitudes in maximally supersymmetric Yang-Mills theory. However, to define it quantum mechanically, one is forced to regularize it since perturbative loop diagrams are not well defined due to presence of ultraviolet divergences stemming from integration in the vicinity of the cusps. A regularization that is adopted by practitioners by allowing one to use spinor helicity formalism, on the one hand, and systematically go to higher orders of perturbation theory is based on a version of dimensional regularization, known as Four-Dimensional Helicity scheme. Recently it was demonstrated that its use for the super Wilson loop at one loop breaks both conformal symmetry and Poincaré supersymmetry. Presently, we exhibit the origin for these effects and demonstrate how one can undo this breaking. The phenomenon is alike the one emerging in renormalization group mixing of conformal operators in conformal theories when one uses dimensional regularization. The rotation matrix to the diagonal basis is found by means of computing the anomaly in the Ward identity for the conformal boost. Presently, we apply this ideology to the super Wilson loop. We compute the one-loop conformal anomaly for the super Wilson loop and find that the anomaly depends on its Grassmann coordinates. By subtracting this anomalous contribution from the super Wilson loop we restore its interpretation as a dual description for reduced non-MHV amplitudes which are expressed in terms of superconformal invariants.

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T25 Quantum field theory on lattices
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T50 Anomalies in quantum field theory
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References:
[1] Brink, L.; Lindgren, O.; Nilsson, B.E.W.; Mandelstam, S., Light cone superspace and the ultraviolet finiteness of the \(N = 4\) model, Nucl. phys. B, Nucl. phys. B, 213, 149, (1983)
[2] Nair, V.P., A current algebra for some gauge theory amplitudes, Phys. lett. B, 214, 215, (1988)
[3] Parke, S.J.; Taylor, T.R., An amplitude for n-gluon scattering, Phys. rev. lett., 56, 2459, (1986)
[4] Witten, E., Perturbative gauge theory as a string theory in twistor space, Commun. math. phys., 252, 189, (2004) · Zbl 1105.81061
[5] Drummond, J.M.; Henn, J.; Korchemsky, G.P.; Sokatchev, E., Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes, Nucl. phys. B, 826, 337, (2010) · Zbl 1203.81175
[6] Drummond, J.M.; Henn, J.M., All tree-level amplitudes in \(N = 4\) SYM, Jhep, 0904, 018, (2009)
[7] Mason, L.J.; Skinner, D., The complete planar S-matrix of \(N = 4\) SYM as a Wilson loop in twistor space, Jhep, 1012, 018, (2010) · Zbl 1294.81122
[8] Caron-Huot, S., Notes on the scattering amplitude/Wilson loop duality, Jhep, 1107, 058, (2011) · Zbl 1298.81357
[9] Harnad, J.P.; Shnider, S.; Ooguri, H.; Rahmfeld, J.; Robins, H.; Tannenhauser, J., Holography in superspace, Commun. math. phys., Jhep, 0007, 045, (2000) · Zbl 0965.81070
[10] Alday, L.F.; Maldacena, J.M.; Alday, L.F.; Maldacena, J.M., Comments on gluon scattering amplitudes via AdS/CFT, Jhep, Jhep, 0711, 068, (2007) · Zbl 1245.81256
[11] Korchemsky, G.P.; Drummond, J.M.; Sokatchev, E., Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. phys. B, 795, 385, (2008) · Zbl 1219.81227
[12] Brandhuber, A.; Heslop, P.; Travaglini, G., MHV amplitudes in \(N = 4\) super-Yang-Mills and Wilson loops, Nucl. phys. B, 794, 231, (2008) · Zbl 1273.81201
[13] Drummond, J.M.; Henn, J.; Korchemsky, G.P.; Sokatchev, E.; Drummond, J.M.; Henn, J.; Korchemsky, G.P.; Sokatchev, E.; Drummond, J.M.; Henn, J.; Korchemsky, G.P.; Sokatchev, E., Hexagon Wilson \(\text{loop} = \text{six-gluon}\) MHV amplitude, Nucl. phys. B, Phys. lett. B, Nucl. phys. B, 815, 142, (2009) · Zbl 1194.81316
[14] Anastasiou, C.; Bern, Z.; Dixon, L.J.; Kosower, D.A., Planar amplitudes in maximally supersymmetric Yang-Mills theory, Phys. rev. lett., 91, 251602, (2003)
[15] Bern, Z.; Dixon, L.J.; Smirnov, V.A., Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. rev. D, 72, 085001, (2005)
[16] Anastasiou, C.; Brandhuber, A.; Heslop, P.; Khoze, V.V.; Spence, B.; Travaglini, G., Two-loop polygon Wilson loops in \(N = 4\) SYM, Jhep, 0905, 115, (2009)
[17] Del Duca, V.; Duhr, C.; Smirnov, V.A.; Del Duca, V.; Duhr, C.; Smirnov, V.A., The two-loop hexagon Wilson loop in \(N = 4\) SYM, Jhep, Jhep, 1005, 084, (2010) · Zbl 1287.81080
[18] Goncharov, A.B.; Spradlin, M.; Vergu, C.; Volovich, A., Classical polylogarithms for amplitudes and Wilson loops, Phys. rev. lett., 105, 151605, (2010)
[19] Bern, Z.; Dixon, L.J.; Kosower, D.A.; Roiban, R.; Spradlin, M.; Vergu, C.; Volovich, A., The two-loop six-gluon MHV amplitude in maximally supersymmetric Yang-Mills theory, Phys. rev. D, 78, 045007, (2008)
[20] Cachazo, F.; Spradlin, M.; Volovich, A., Leading singularities of the two-loop six-particle MHV amplitude, Phys. rev. D, 78, 105022, (2008)
[21] Belitsky, A.V.; Korchemsky, G.P.; Sokatchev, E., Are scattering amplitudes dual to super Wilson loops?, Nucl. phys. B, 855, 333, (2012) · Zbl 1229.81176
[22] Bern, Z.; De Freitas, A.; Dixon, L.J.; Wong, H.L., Supersymmetric regularization, two loop QCD amplitudes and coupling shifts, Phys. rev. D, 66, 085002, (2002)
[23] Eden, B.; Heslop, P.; Korchemsky, G.P.; Sokatchev, E.; Eden, B.; Heslop, P.; Korchemsky, G.P.; Sokatchev, E., The super-correlator/super-amplitude duality: part II · Zbl 1262.81197
[24] Eden, B.; Korchemsky, G.P.; Sokatchev, E.; Alday, L.F.; Eden, B.; Korchemsky, G.P.; Maldacena, J.; Sokatchev, E., From correlation functions to Wilson loops, Jhep, Jhep, 1109, 123, (2011) · Zbl 1301.81096
[25] Ferrara, S.; Gatto, R.; Grillo, A.F., Conformal algebra in space-time and operator product expansion, Springer tracts mod. phys., 67, 1, (1973)
[26] Müller, D.; Belitsky, A.V.; Müller, D., Broken conformal invariance and spectrum of anomalous dimensions in QCD, Phys. rev. D, Nucl. phys. B, 537, 397, (1999)
[27] Hodges, A., Eliminating spurious poles from gauge-theoretic amplitudes · Zbl 1342.81291
[28] Drummond, J.M.; Henn, J.; Korchemsky, G.P.; Sokatchev, E., Generalized unitarity for \(N = 4\) super-amplitudes · Zbl 1262.81195
[29] Britto, R.; Feng, B.; Roiban, R.; Spradlin, M.; Volovich, A., All split helicity tree-level gluon amplitudes, Phys. rev. D, 71, 105017, (2005)
[30] Britto, R.; Cachazo, F.; Feng, B.; Britto, R.; Cachazo, F.; Feng, B.; Witten, E., Direct proof of tree-level recursion relation in Yang-Mills theory, Nucl. phys. B, Phys. rev. lett., 94, 181602, (2005)
[31] Mangano, M.L.; Parke, S.J.; Xu, Z., Duality and multigluon scattering, Nucl. phys. B, 298, 653, (1988)
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