×

Event shapes in \(\mathcal{N} = 4\) super-Yang-Mills theory. (English) Zbl 1323.81056

Summary: We study event shapes in \(\mathcal{N} = 4 \text{ SYM}\) describing the angular distribution of energy and \(R\)-charge in the final states created by the simplest half-BPS scalar operator. Applying the approach developed in the companion paper [the authors, “From correlation functions to event shapes”, 40 p. (2014), arXiv:1309.0769], we compute these observables using the correlation functions of certain components of the \(\mathcal{N} = 4\) stress-tensor supermultiplet: the half-BPS operator itself, the \(R\)-symmetry current and the stress tensor. We present master formulas for the all-order event shapes as convolutions of the Mellin amplitude defining the correlation function of the half-BPS operators, with a coupling-independent kernel determined by the choice of the observable. We find remarkably simple relations between various event shapes following from \(\mathcal{N} = 4\) superconformal symmetry. We perform thorough checks at leading order in the weak coupling expansion and show perfect agreement with the conventional calculations based on amplitude techniques. We extend our results to strong coupling using the correlation function of half-BPS operators obtained from the AdS/CFT correspondence.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81V05 Strong interaction, including quantum chromodynamics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory

Software:

xCore; Spinors; xAct

References:

[1] Sterman, G. F.; Weinberg, S., Jets from quantum chromodynamics, Phys. Rev. Lett., 39, 1436 (1977)
[2] Kunszt, Z.; Nason, P.; Marchesini, G.; Webber, B. R., QCD at LEP, (Proceedings, Z Physics at LEP 1, vol. 1. Proceedings, Z Physics at LEP 1, vol. 1, Geneva (1989)), 373-453
[3] Biebel, O., Experimental tests of the strong interaction and its energy dependence in electron positron annihilation, Phys. Rep., 340, 165 (2001)
[4] Basham, C. L.; Brown, L. S.; Ellis, S. D.; Love, S. T., Energy correlations in electron-positron annihilation in Quantum Chromodynamics: asymptotically free perturbation theory, Phys. Rev. D, 19, 2018 (1979)
[5] Dasgupta, M.; Salam, G. P., Event shapes in \(e^+ e^-\) annihilation and deep inelastic scattering, J. Phys. G, 30, R143 (2004)
[6] Kinoshita, T., Mass singularities of Feynman amplitudes, J. Math. Phys., 3, 650 (1962) · Zbl 0118.44501
[7] Lee, T. D.; Nauenberg, M., Degenerate systems and mass singularities, Phys. Rev., 133, B1549 (1964)
[8] van Neerven, W. L., Infrared behavior of on-shell form-factors in \(N = 4\) supersymmetric Yang-Mills field theory, Z. Phys. C, 30, 595 (1986)
[9] Sveshnikov, N. A.; Tkachov, F. V., Jets and quantum field theory, Phys. Lett. B, 382, 403 (1996)
[10] Korchemsky, G. P.; Oderda, G.; Sterman, G. F., Power corrections and nonlocal operators
[11] Korchemsky, G. P.; Sterman, G. F., Power corrections to event shapes and factorization, Nucl. Phys. B, 555, 335 (1999)
[12] Belitsky, A. V.; Korchemsky, G. P.; Sterman, G., Energy flow in QCD and event shape functions, Phys. Lett. B, 515, 297 (2001)
[13] Hofman, D. M.; Maldacena, J., Conformal collider physics: energy and charge correlations, J. High Energy Phys., 0805 (2008), 012
[14] Belitsky, A. V.; Hohenegger, S.; Korchemsky, G. P.; Sokatchev, E.; Zhiboedov, A., From correlation functions to event shapes · Zbl 1323.81084
[15] Howe, P. S.; West, P. C., Operator product expansions in four-dimensional superconformal field theories, Phys. Lett. B, 389, 273 (1996)
[16] D’Hoker, E.; Freedman, D. Z.; Skiba, W., Field theory tests for correlators in the AdS/CFT correspondence, Phys. Rev. D, 59 (1999), 045008
[17] Howe, P. S.; Sokatchev, E.; West, P. C., Three point functions in \(N = 4\) Yang-Mills, Phys. Lett. B, 444, 341 (1998)
[18] Lee, S.; Minwalla, S.; Rangamani, M.; Seiberg, N., Three point functions of chiral operators in \(D = 4, N = 4 \text{ SYM}\) at large \(N\), Adv. Theor. Math. Phys., 2, 697 (1998) · Zbl 0923.53033
[19] Penati, S.; Santambrogio, A.; Zanon, D., More on correlators and contact terms in \(N = 4 \text{ SYM}\) at order \(g^4\), Nucl. Phys. B, 593, 651 (2001) · Zbl 0971.81520
[20] Collins, J. C., Sudakov form-factors, Adv. Ser. Dir. High Energy Phys., 5, 573 (1989) · Zbl 0961.81525
[21] Kunszt, Z.; Soper, D. E., Calculation of jet cross sections in hadron collisions at order \(\alpha_s^3\), Phys. Rev. D, 46, 192 (1992)
[22] Galperin, A.; Ivanov, E.; Kalitsyn, S.; Ogievetsky, V.; Sokatchev, E., Unconstrained \(N = 2\) matter, Yang-Mills and supergravity theories in harmonic superspace, Class. Quantum Gravity, 1, 469 (1984)
[23] Howe, P. S.; Hartwell, G. G., A superspace survey, Class. Quantum Gravity, 12, 1823 (1995) · Zbl 0828.32007
[24] Banfi, A.; Salam, G. P.; Zanderighi, G., Infrared safe definition of jet flavor, Eur. Phys. J. C, 47, 113 (2006)
[25] Collins, J. C.; Soper, D. E., Back-to-back jets: Fourier transform from B to K-transverse, Nucl. Phys. B, 197, 446 (1982)
[26] Engelund, O. T.; Roiban, R., Correlation functions of local composite operators from generalized unitarity, J. High Energy Phys., 1303 (2013), 172 · Zbl 1342.81278
[27] Eden, B.; Howe, P. S.; West, P. C., Nilpotent invariants in \(N = 4\) SYM, Phys. Lett. B, 463, 19 (1999) · Zbl 0987.81102
[28] Eden, B.; Howe, P. S.; Schubert, C.; Sokatchev, E.; West, P. C., Extremal correlators in four-dimensional SCFT, Phys. Lett. B, 472, 323 (2000) · Zbl 0959.81100
[29] Gonzalez-Rey, F.; Park, I. Y.; Schalm, K., A note on four point functions of conformal operators in \(N = 4\) superYang-Mills, Phys. Lett. B, 448, 37 (1999) · Zbl 1058.81708
[30] Eden, B.; Howe, P. S.; Schubert, C.; Sokatchev, E.; West, P. C., Four point functions in \(N = 4\) supersymmetric Yang-Mills theory at two loops, Nucl. Phys. B, 557, 355 (1999) · Zbl 1068.81602
[31] Eden, B.; Howe, P. S.; Schubert, C.; Sokatchev, E.; West, P. C., Simplifications of four point functions in \(N = 4\) supersymmetric Yang-Mills theory at two loops, Phys. Lett. B, 466, 20 (1999) · Zbl 0971.81156
[32] Eden, B.; Petkou, A. C.; Schubert, C.; Sokatchev, E., Partial nonrenormalization of the stress tensor four point function in \(N = 4\) SYM and AdS/CFT, Nucl. Phys. B, 607, 191 (2001) · Zbl 0969.81576
[33] Eden, B.; Schubert, C.; Sokatchev, E., Three loop four point correlator in \(N = 4\) SYM, Phys. Lett. B, 482, 309 (2000) · Zbl 0990.81121
[34] Bianchi, M.; Kovacs, S.; Rossi, G.; Stanev, Y. S., Anomalous dimensions in \(N = 4\) SYM theory at order \(g^4\), Nucl. Phys. B, 584, 216 (2000) · Zbl 0984.81155
[35] Usyukina, N. I.; Davydychev, A. I., Some exact results for two loop diagrams with three and four external lines, Phys. At. Nucl.. Phys. At. Nucl., Yad. Fiz., 56, 11, 172 (1993)
[36] Luscher, M.; Mack, G., Global conformal invariance in Quantum Field Theory, Commun. Math. Phys., 41, 203 (1975)
[37] Mack, G., D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
[38] Arutyunov, G.; Frolov, S., Scalar quartic couplings in type IIB supergravity on AdS(5) × \(S^5\), Nucl. Phys. B, 579, 117 (2000) · Zbl 0992.83085
[39] Arutyunov, G.; Frolov, S., Four point functions of lowest weight CPOs in \(N = 4\) SYM(4) in supergravity approximation, Phys. Rev. D, 62 (2000), 064016
[40] Arutyunov, G.; Frolov, S.; Petkou, A. C., Nucl. Phys. B, 609, 539 (2001), (Erratum)
[41] Martin-Garcia, J. M., xAct: efficient tensor computer algebra
[42] Gomez-Lobo, A. G.-P.; Martin-Garcia, J. M., Spinors: a Mathematica package for doing spinor calculus in General Relativity, Comput. Phys. Commun., 183, 2214 (2012) · Zbl 1296.83004
[44] Eden, B.; Heslop, P.; Korchemsky, G. P.; Sokatchev, E., Hidden symmetry of four-point correlation functions and amplitudes in \(N = 4\) SYM, Nucl. Phys. B, 862, 193 (2012) · Zbl 1246.81322
[45] Keldysh, L. V., Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz.. Zh. Eksp. Teor. Fiz., Sov. Phys. JETP, 20, 1018 (1965)
[46] Belitsky, A. V.; Derkachov, S. E.; Korchemsky, G. P.; Manashov, A. N., Superconformal operators in \(N = 4\) superYang-Mills theory, Phys. Rev. D, 70 (2004), 045021
[47] Nirschl, M.; Osborn, H., Superconformal Ward identities and their solution, Nucl. Phys. B, 711, 409 (2005) · Zbl 1109.81350
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.