Abstract
We derive the explicit expression for the four-point correlation function of stress-energy tensors in four-dimensional \( \mathcal{N}=4 \) superconformal theory. We show that it has a remarkably simple and suggestive form allowing us to predict a large class of four-point correlation functions involving the stress-energy tensor and other conserved currents. We then apply the obtained results on the correlation functions to computing the energy-energy correlations, which measure the flow of energy in the final states created from the vacuum by a source. We demonstrate that they are given by a universal function independent of the choice of the source. Our analysis relies only on \( \mathcal{N}=4 \) superconformal symmetry and does not use the dynamics of the theory.
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References
Y.S. Stanev, Stress-energy tensor and U(1) current operator product expansions in conformal QFT, Bulg. J. Phys. 15 (1988) 93 [INSPIRE].
H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning conformal correlators, JHEP 11 (2011) 071 [arXiv:1107.3554] [INSPIRE].
A. Dymarsky, On the four-point function of the stress-energy tensors in a CFT, JHEP 10 (2015) 075 [arXiv:1311.4546] [INSPIRE].
F.A. Dolan and H. Osborn, Superconformal symmetry, correlation functions and the operator product expansion, Nucl. Phys. B 629 (2002) 3 [hep-th/0112251] [INSPIRE].
P.S. Howe and P.C. West, Superconformal invariants and extended supersymmetry, Phys. Lett. B 400 (1997) 307 [hep-th/9611075] [INSPIRE].
J.-H. Park, Superconformal symmetry and correlation functions, Nucl. Phys. B 559 (1999) 455 [hep-th/9903230] [INSPIRE].
B. Eden, P.S. Howe and P.C. West, Nilpotent invariants in N = 4 SYM, Phys. Lett. B 463 (1999) 19 [hep-th/9905085] [INSPIRE].
P.J. Heslop and P.S. Howe, Four point functions in N = 4 SYM, JHEP 01 (2003) 043 [hep-th/0211252] [INSPIRE].
F.A. Dolan, L. Gallot and E. Sokatchev, On four-point functions of 1/2-BPS operators in general dimensions, JHEP 09 (2004) 056 [hep-th/0405180] [INSPIRE].
A.V. Belitsky, S. Hohenegger, G.P. Korchemsky and E. Sokatchev, N = 4 superconformal Ward identities for correlation functions, arXiv:1409.2502 [INSPIRE].
C.L. Basham, L.S. Brown, S.D. Ellis and S.T. Love, Energy correlations in electron-positron annihilation: testing QCD, Phys. Rev. Lett. 41 (1978) 1585 [INSPIRE].
F.R. Ore Jr. and G.F. Sterman, An operator approach to weighted cross-sections, Nucl. Phys. B 165 (1980) 93 [INSPIRE].
N.A. Sveshnikov and F.V. Tkachov, Jets and quantum field theory, Phys. Lett. B 382 (1996) 403 [hep-ph/9512370] [INSPIRE].
G.P. Korchemsky, G. Oderda and G.F. Sterman, Power corrections and nonlocal operators, hep-ph/9708346 [INSPIRE].
G.P. Korchemsky and G.F. Sterman, Power corrections to event shapes and factorization, Nucl. Phys. B 555 (1999) 335 [hep-ph/9902341] [INSPIRE].
A.V. Belitsky, G.P. Korchemsky and G.F. Sterman, Energy flow in QCD and event shape functions, Phys. Lett. B 515 (2001) 297 [hep-ph/0106308] [INSPIRE].
A.V. Belitsky, S. Hohenegger, G.P. Korchemsky, E. Sokatchev and A. Zhiboedov, From correlation functions to event shapes, Nucl. Phys. B 884 (2014) 305 [arXiv:1309.0769] [INSPIRE].
A.V. Belitsky, S. Hohenegger, G.P. Korchemsky, E. Sokatchev and A. Zhiboedov, Event shapes in \( \mathcal{N}=4 \) super-Yang-Mills theory, Nucl. Phys. B 884 (2014) 206 [arXiv:1309.1424] [INSPIRE].
D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
A.V. Belitsky, S. Hohenegger, G.P. Korchemsky, E. Sokatchev and A. Zhiboedov, Energy-energy correlations in \( \mathcal{N}=4 \) supersymmetric Yang-Mills theory, Phys. Rev. Lett. 112 (2014) 071601 [arXiv:1311.6800] [INSPIRE].
V. Gonçalves, Four point function of \( \mathcal{N}=4 \) stress-tensor multiplet at strong coupling, JHEP 04 (2015) 150 [arXiv:1411.1675] [INSPIRE].
S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, \( \mathcal{N}=4 \) SYM at large N, Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].
E. D’Hoker, D.Z. Freedman and W. Skiba, Field theory tests for correlators in the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 045008 [hep-th/9807098] [INSPIRE].
P.S. Howe, E. Sokatchev and P.C. West, Three point functions in \( \mathcal{N}=4 \) Yang-Mills, Phys. Lett. B 444 (1998) 341 [hep-th/9808162] [INSPIRE].
S. Penati, A. Santambrogio and D. Zanon, Two point functions of chiral operators in \( \mathcal{N}=4 \) SYM at order g 4, JHEP 12 (1999) 006 [hep-th/9910197] [INSPIRE].
S. Penati, A. Santambrogio and D. Zanon, More on correlators and contact terms in \( \mathcal{N}=4 \) SYM at order g 4, Nucl. Phys. B 593 (2001) 651 [hep-th/0005223] [INSPIRE].
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] [INSPIRE].
S. Giombi, S. Prakash and X. Yin, A note on CFT correlators in three dimensions, JHEP 07 (2013) 105 [arXiv:1104.4317] [INSPIRE].
I. Todorov, Conformal field theories with infinitely many conservation laws, J. Math. Phys. 54 (2013) 022303 [arXiv:1207.3661] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Hidden symmetry of four-point correlation functions and amplitudes in N = 4 SYM, Nucl. Phys. B 862 (2012) 193 [arXiv:1108.3557] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N = 4 SYM, Nucl. Phys. B 862 (2012) 450 [arXiv:1201.5329] [INSPIRE].
F. Gonzalez-Rey, I.Y. Park and K. Schalm, A note on four point functions of conformal operators in N = 4 super Yang-Mills, Phys. Lett. B 448 (1999) 37 [hep-th/9811155] [INSPIRE].
B. Eden, C. Schubert and E. Sokatchev, Three loop four point correlator in N = 4 SYM, Phys. Lett. B 482 (2000) 309 [hep-th/0003096] [INSPIRE].
M. Bianchi, S. Kovacs, G. Rossi and Y.S. Stanev, Anomalous dimensions in \( \mathcal{N}=4 \) SYM theory at order g 4, Nucl. Phys. B 584 (2000) 216 [hep-th/0003203] [INSPIRE].
J. Drummond et al., Leading singularities and off-shell conformal integrals, JHEP 08 (2013) 133 [arXiv:1303.6909] [INSPIRE].
G. Arutyunov and S. Frolov, Scalar quartic couplings in type IIB supergravity on AdS 5 × S 5, Nucl. Phys. B 579 (2000) 117 [hep-th/9912210] [INSPIRE].
G. Arutyunov and S. Frolov, Four-point functions of lowest weight chiral primary operators in N = 4 four-dimensional supersymmetric Yang-Mills theory in the supergravity approximation, Phys. Rev. D 62 (2000) 064016 [hep-th/0002170] [INSPIRE].
G. Arutyunov, S. Frolov and A.C. Petkou, Operator product expansion of the lowest weight CPOs in \( \mathcal{N}=4 \) SYM 4 at strong coupling, Nucl. Phys. B 586 (2000) 547 [Erratum ibid. B 609 (2001) 539] [hep-th/0005182] [INSPIRE].
P.S. Howe and P.C. West, Operator product expansions in four-dimensional superconformal field theories, Phys. Lett. B 389 (1996) 273 [hep-th/9607060] [INSPIRE].
E.S. Fradkin and M.Y. Palchik, Recent developments in conformal invariant quantum field theory, Phys. Rept. 44 (1978) 249 [INSPIRE].
J. Erdmenger and H. Osborn, Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions, Nucl. Phys. B 483 (1997) 431 [hep-th/9605009] [INSPIRE].
L.J. Mason and D. Skinner, Dual superconformal invariance, momentum twistors and Grassmannians, JHEP 11 (2009) 045 [arXiv:0909.0250] [INSPIRE].
N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The all-loop integrand for scattering amplitudes in planar \( \mathcal{N}=4 \) SYM, JHEP 01 (2011) 041 [arXiv:1008.2958] [INSPIRE].
J.M. Drummond, L. Gallot and E. Sokatchev, Superconformal invariants or how to relate four-point AdS amplitudes, Phys. Lett. B 645 (2007) 95 [hep-th/0610280] [INSPIRE].
E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Graviton exchange and complete four point functions in the AdS/CFT correspondence, Nucl. Phys. B 562 (1999) 353 [hep-th/9903196] [INSPIRE].
L. Cornalba, Eikonal methods in AdS/CFT: Regge theory and multi-reggeon exchange, arXiv:0710.5480 [INSPIRE].
D. Chicherin et al., Correlation functions of the chiral stress-tensor multiplet in \( \mathcal{N}=4 \) SYM, JHEP 06 (2015) 198 [arXiv:1412.8718] [INSPIRE].
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Korchemsky, G.P., Sokatchev, E. Four-point correlation function of stress-energy tensors in \( \mathcal{N}=4 \) superconformal theories. J. High Energ. Phys. 2015, 1–33 (2015). https://doi.org/10.1007/JHEP12(2015)133
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DOI: https://doi.org/10.1007/JHEP12(2015)133