The single copy of the gravitational holonomy. (English) Zbl 1476.83037
Summary: The double copy is a well-established relationship between gravity and gauge theories. It relates perturbative scattering amplitudes as well as classical solutions, and recently there has been mounting evidence that it also applies to non-perturbative information. In this paper, we consider the holonomy properties of manifolds in gravity and prescribe a single copy of gravitational holonomy that differs from the holonomy in gauge theory. We discuss specific cases and give examples where the single copy holonomy group is reduced. Our results may prove useful in extending the classical double copy. We also clarify previous misconceptions in the literature regarding gravitational Wilson lines and holonomy.
MSC:
| 83C45 | Quantization of the gravitational field |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
| 81Q70 | Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory |
References:
| [1] | Bern, Z.; Carrasco, JJM; Johansson, H., Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett., 105 (2010) · doi:10.1103/PhysRevLett.105.061602 |
| [2] | Bern, Z.; Dennen, T.; Huang, Y-t; Kiermaier, M., Gravity as the Square of Gauge Theory, Phys. Rev. D, 82 (2010) · doi:10.1103/PhysRevD.82.065003 |
| [3] | White, CD, Exact solutions for the biadjoint scalar field, Phys. Lett. B, 763, 365 (2016) · Zbl 1370.70053 · doi:10.1016/j.physletb.2016.10.052 |
| [4] | De Smet, P-J; White, CD, Extended solutions for the biadjoint scalar field, Phys. Lett. B, 775, 163 (2017) · Zbl 1380.81227 · doi:10.1016/j.physletb.2017.11.007 |
| [5] | Bahjat-Abbas, N.; Stark-Muchão, R.; White, CD, Biadjoint wires, Phys. Lett. B, 788, 274 (2019) · Zbl 1405.81071 · doi:10.1016/j.physletb.2018.11.026 |
| [6] | Bahjat-Abbas, N.; Stark-Muchão, R.; White, CD, Monopoles, shockwaves and the classical double copy, JHEP, 04, 102 (2020) · Zbl 1436.83014 · doi:10.1007/JHEP04(2020)102 |
| [7] | Berman, DS; Kim, K.; Lee, K., The classical double copy for M-theory from a Kerr-Schild ansatz for exceptional field theory, JHEP, 04, 071 (2021) · Zbl 1462.83080 · doi:10.1007/JHEP04(2021)071 |
| [8] | Monteiro, R.; O’Connell, D., The Kinematic Algebra From the Self-Dual Sector, JHEP, 07, 007 (2011) · Zbl 1298.81401 · doi:10.1007/JHEP07(2011)007 |
| [9] | Borsten, L.; Jurčo, B.; Kim, H.; Macrelli, T.; Sämann, C.; Wolf, M., Double Copy from Homotopy Algebras, Fortsch. Phys., 69, 2100075 (2021) · Zbl 1537.83165 · doi:10.1002/prop.202100075 |
| [10] | Chacón, E.; García-Compeán, H.; Luna, A.; Monteiro, R.; White, CD, New heavenly double copies, JHEP, 03, 247 (2021) · Zbl 1461.83004 · doi:10.1007/JHEP03(2021)247 |
| [11] | White, CD, Twistorial Foundation for the Classical Double Copy, Phys. Rev. Lett., 126 (2021) · doi:10.1103/PhysRevLett.126.061602 |
| [12] | Chacón, E.; Nagy, S.; White, CD, The Weyl double copy from twistor space, JHEP, 05, 2239 (2021) · Zbl 1466.83062 · doi:10.1007/JHEP05(2021)239 |
| [13] | K. Farnsworth, M. L. Graesser and G. Herczeg, Twistor Space Origins of the Newman-Penrose Map, arXiv:2104.09525 [INSPIRE]. · Zbl 1457.83031 |
| [14] | Alawadhi, R.; Berman, DS; Spence, B.; Peinador Veiga, D., S-duality and the double copy, JHEP, 03, 059 (2020) · Zbl 1435.81225 · doi:10.1007/JHEP03(2020)059 |
| [15] | Huang, Y-T; Kol, U.; O’Connell, D., Double copy of electric-magnetic duality, Phys. Rev. D, 102 (2020) · doi:10.1103/PhysRevD.102.046005 |
| [16] | N. Moynihan and J. Murugan, On-Shell Electric-Magnetic Duality and the Dual Graviton, arXiv:2002.11085 [INSPIRE]. |
| [17] | Kim, J-W; Shim, M., Gravitational Dyonic Amplitude at One-Loop and its Inconsistency with the Classical Impulse, JHEP, 02, 217 (2021) · doi:10.1007/JHEP02(2021)217 |
| [18] | Berman, DS; Chacón, E.; Luna, A.; White, CD, The self-dual classical double copy, and the Eguchi-Hanson instanton, JHEP, 01, 107 (2019) · Zbl 1409.83137 · doi:10.1007/JHEP01(2019)107 |
| [19] | Alfonsi, L.; White, CD; Wikeley, S., Topology and Wilson lines: global aspects of the double copy, JHEP, 07, 091 (2020) · Zbl 1451.83006 · doi:10.1007/JHEP07(2020)091 |
| [20] | S. S. Wani, T. S. Tsun and M. Faizal, Dualized Gravity beyond Linear Approximation, arXiv:2103.02444 [INSPIRE]. |
| [21] | Modanese, G., Geodesic round trips by parallel transport in quantum gravity, Phys. Rev. D, 47, 502 (1993) · doi:10.1103/PhysRevD.47.502 |
| [22] | Modanese, G., Wilson loops in four-dimensional quantum gravity, Phys. Rev. D, 49, 6534 (1994) · doi:10.1103/PhysRevD.49.6534 |
| [23] | Hamber, HW; Williams, RM, Gravitational Wilson loop and large scale curvature, Phys. Rev. D, 76 (2007) · doi:10.1103/PhysRevD.76.084008 |
| [24] | Hamber, HW; Williams, RM, Gravitational Wilson Loop in Discrete Quantum Gravity, Phys. Rev. D, 81 (2010) · doi:10.1103/PhysRevD.81.084048 |
| [25] | Mandelstam, S., Quantization of the gravitational field, Annals Phys., 19, 25 (1962) · Zbl 0109.20905 · doi:10.1016/0003-4916(62)90233-6 |
| [26] | Brandhuber, A.; Heslop, P.; Nasti, A.; Spence, B.; Travaglini, G., Four-point Amplitudes in N = 8 Supergravity and Wilson Loops, Nucl. Phys. B, 807, 290 (2009) · Zbl 1192.83064 · doi:10.1016/j.nuclphysb.2008.09.010 |
| [27] | Hamber, HW; Williams, RM, Newtonian potential in quantum Regge gravity, Nucl. Phys. B, 435, 361 (1995) · doi:10.1016/0550-3213(94)00495-Z |
| [28] | Naculich, SG; Schnitzer, HJ, Eikonal methods applied to gravitational scattering amplitudes, JHEP, 05, 087 (2011) · Zbl 1296.83028 · doi:10.1007/JHEP05(2011)087 |
| [29] | White, CD, Factorization Properties of Soft Graviton Amplitudes, JHEP, 05, 060 (2011) · Zbl 1296.83030 · doi:10.1007/JHEP05(2011)060 |
| [30] | Miller, DJ; White, CD, The Gravitational cusp anomalous dimension from AdS space, Phys. Rev. D, 85, 104034 (2012) · doi:10.1103/PhysRevD.85.104034 |
| [31] | Dowker, JS; Roche, JA, The Gravitational analogues of magnetic monopoles, Proc. Phys. Soc., 92, 1 (1967) · doi:10.1088/0370-1328/92/1/302 |
| [32] | Melville, S.; Naculich, SG; Schnitzer, HJ; White, CD, Wilson line approach to gravity in the high energy limit, Phys. Rev. D, 89 (2014) · doi:10.1103/PhysRevD.89.025009 |
| [33] | Luna, A.; Melville, S.; Naculich, SG; White, CD, Next-to-soft corrections to high energy scattering in QCD and gravity, JHEP, 01, 052 (2017) · Zbl 1373.83045 · doi:10.1007/JHEP01(2017)052 |
| [34] | Oxburgh, S.; White, CD, BCJ duality and the double copy in the soft limit, JHEP, 02, 127 (2013) · Zbl 1342.81719 · doi:10.1007/JHEP02(2013)127 |
| [35] | Sabio Vera, A.; Serna Campillo, E.; Vazquez-Mozo, MA, Color-Kinematics Duality and the Regge Limit of Inelastic Amplitudes, JHEP, 04, 086 (2013) · doi:10.1007/JHEP04(2013)086 |
| [36] | H. Johansson, A. Sabio Vera, E. Serna Campillo and M. A. Vazquez-Mozo, Color-kinematics duality and dimensional reduction for graviton emission in Regge limit, in International Workshop on Low X Physics, (2013) [arXiv:1310.1680] [INSPIRE]. |
| [37] | Plefka, J.; Steinhoff, J.; Wormsbecher, W., Effective action of dilaton gravity as the classical double copy of Yang-Mills theory, Phys. Rev. D, 99 (2019) · doi:10.1103/PhysRevD.99.024021 |
| [38] | M. Berger, Sur les groupes d’holonomie homogènes de variétés à connexion affine et des variétés riemanniennes, Bull. Soc. Math. Fr.83 (1955) 279. · Zbl 0068.36002 |
| [39] | Galaev, AS, Holonomy groups of Lorentzian manifolds, Russ. Math. Surveys, 70, 249 (2015) · Zbl 1332.53065 · doi:10.1070/RM2015v070n02ABEH004947 |
| [40] | A. L. Besse, Einstein Manifolds, Springer-Verlag, Berlin, Heidelberg, New York (1987). · Zbl 0613.53001 |
| [41] | S. M. Carroll, Spacetime and Geometry, Cambridge University Press (2019). · Zbl 1418.83001 |
| [42] | I. A. Korchemskaya and G. P. Korchemsky, High-energy scattering in QCD and cross singularities of Wilson loops, Nucl. Phys. B437 (1995) 127 [hep-ph/9409446] [INSPIRE]. |
| [43] | Monteiro, R.; O’Connell, D.; White, CD, Black holes and the double copy, JHEP, 12, 056 (2014) · Zbl 1333.83048 · doi:10.1007/JHEP12(2014)056 |
| [44] | Levi, M., Effective Field Theories of Post-Newtonian Gravity: A comprehensive review, Rept. Prog. Phys., 83 (2020) · doi:10.1088/1361-6633/ab12bc |
| [45] | Hanson, AJ; Regge, T., The Relativistic Spherical Top, Annals Phys., 87, 498 (1974) · doi:10.1016/0003-4916(74)90046-3 |
| [46] | Bailey, I.; Israel, W., Lagrangian Dynamics of Spinning Particles and Polarized Media in General Relativity, Commun. Math. Phys., 42, 65 (1975) · doi:10.1007/BF01609434 |
| [47] | W. G. Dixon, Dynamics of extended bodies in general relativity. I. Momentum and angular momentum, Proc. Roy. Soc. Lond. A314 (1970) 499 [INSPIRE]. |
| [48] | A. Papapetrou, Spinning test particles in general relativity. 1, Proc. Roy. Soc. Lond. A209 (1951) 248 [INSPIRE]. · Zbl 0044.22801 |
| [49] | J. Vines, D. Kunst, J. Steinhoff and T. Hinderer, Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin, Phys. Rev. D93 (2016) 103008 [Erratum ibid.104 (2021) 029902] [arXiv:1601.07529] [INSPIRE]. |
| [50] | Li, J.; Prabhu, SG, Gravitational radiation from the classical spinning double copy, Phys. Rev. D, 97, 105019 (2018) · doi:10.1103/PhysRevD.97.105019 |
| [51] | Goldberger, WD; Li, J.; Prabhu, SG, Spinning particles, axion radiation, and the classical double copy, Phys. Rev. D, 97, 105018 (2018) · doi:10.1103/PhysRevD.97.105018 |
| [52] | Chung, M-Z; Huang, Y-T; Kim, J-W; Lee, S., The simplest massive S-matrix: from minimal coupling to Black Holes, JHEP, 04, 156 (2019) · Zbl 1415.83014 · doi:10.1007/JHEP04(2019)156 |
| [53] | Chung, M-Z; Huang, Y-T; Kim, J-W, Kerr-Newman stress-tensor from minimal coupling, JHEP, 12, 103 (2020) · Zbl 1457.83029 · doi:10.1007/JHEP12(2020)103 |
| [54] | Arkani-Hamed, N.; Huang, Y-t; O’Connell, D., Kerr black holes as elementary particles, JHEP, 01, 046 (2020) · Zbl 1434.83049 · doi:10.1007/JHEP01(2020)046 |
| [55] | W. T. Emond, Y.-T. Huang, U. Kol, N. Moynihan and D. O’Connell, Amplitudes from Coulomb to Kerr-Taub-NUT, arXiv:2010.07861 [INSPIRE]. |
| [56] | Guevara, A.; Maybee, B.; Ochirov, A.; O’connell, D.; Vines, J., A worldsheet for Kerr, JHEP, 03, 201 (2021) · Zbl 1461.83030 · doi:10.1007/JHEP03(2021)201 |
| [57] | Guevara, A.; Ochirov, A.; Vines, J., Scattering of Spinning Black Holes from Exponentiated Soft Factors, JHEP, 09, 056 (2019) · Zbl 1423.83030 · doi:10.1007/JHEP09(2019)056 |
| [58] | Guevara, A.; Ochirov, A.; Vines, J., Black-hole scattering with general spin directions from minimal-coupling amplitudes, Phys. Rev. D, 100, 104024 (2019) · doi:10.1103/PhysRevD.100.104024 |
| [59] | Y. F. Bautista and A. Guevara, From Scattering Amplitudes to Classical Physics: Universality, Double Copy and Soft Theorems, arXiv:1903.12419 [INSPIRE]. |
| [60] | Weinberg, S., Infrared photons and gravitons, Phys. Rev., 140, B516 (1965) · doi:10.1103/PhysRev.140.B516 |
| [61] | Gross, DJ; Jackiw, R., Low-Energy Theorem for Graviton Scattering, Phys. Rev., 166, 1287 (1968) · doi:10.1103/PhysRev.166.1287 |
| [62] | Low, FE, Bremsstrahlung of very low-energy quanta in elementary particle collisions, Phys. Rev., 110, 974 (1958) · Zbl 0082.42802 · doi:10.1103/PhysRev.110.974 |
| [63] | Burnett, TH; Kroll, NM, Extension of the low soft photon theorem, Phys. Rev. Lett., 20, 86 (1968) · doi:10.1103/PhysRevLett.20.86 |
| [64] | Del Duca, V., High-energy Bremsstrahlung Theorems for Soft Photons, Nucl. Phys. B, 345, 369 (1990) · doi:10.1016/0550-3213(90)90392-Q |
| [65] | F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE]. |
| [66] | Casali, E., Soft sub-leading divergences in Yang-Mills amplitudes, JHEP, 08, 077 (2014) · doi:10.1007/JHEP08(2014)077 |
| [67] | Laenen, E.; Stavenga, G.; White, CD, Path integral approach to eikonal and next-to-eikonal exponentiation, JHEP, 03, 054 (2009) · doi:10.1088/1126-6708/2009/03/054 |
| [68] | T. Rothman, G. F. R. Ellis and J. Murugan, Holonomy in the Schwarzschild-Droste geometry, Class. Quant. Grav.18 (2001) 1217 [gr-qc/0008070] [INSPIRE]. · Zbl 0981.53015 |
| [69] | Taub, AH, Empty space-times admitting a three parameter group of motions, Annals Math., 53, 472 (1951) · Zbl 0044.22804 · doi:10.2307/1969567 |
| [70] | Newman, E.; Tamburino, L.; Unti, T., Empty space generalization of the Schwarzschild metric, J. Math. Phys., 4, 915 (1963) · Zbl 0115.43305 · doi:10.1063/1.1704018 |
| [71] | Luna, A.; Monteiro, R.; O’Connell, D.; White, CD, The classical double copy for Taub-NUT spacetime, Phys. Lett. B, 750, 272 (2015) · Zbl 1364.83005 · doi:10.1016/j.physletb.2015.09.021 |
| [72] | Chong, ZW; Gibbons, GW; Lü, H.; Pope, CN, Separability and Killing tensors in Kerr-Taub-NUT-de Sitter metrics in higher dimensions, Phys. Lett. B, 609, 124 (2005) · Zbl 1247.83168 · doi:10.1016/j.physletb.2004.07.066 |
| [73] | D. Bini, C. Cherubini and R. T. Jantzen, Circular holonomy in the Taub NUT space-time, Class. Quant. Grav.19 (2002) 5481 [gr-qc/0210003] [INSPIRE]. · Zbl 1039.83007 |
| [74] | A. Luna, The double copy and classical solutions, Ph.D. Thesis, University of Glasgow (2018) [http://theses.gla.ac.uk/id/eprint/8716]. |
| [75] | Monteiro, R.; O’Connell, D., The Kinematic Algebras from the Scattering Equations, JHEP, 03, 110 (2014) · Zbl 1333.81421 · doi:10.1007/JHEP03(2014)110 |
| [76] | Alawadhi, R.; Berman, DS; Spence, B., Weyl doubling, JHEP, 09, 127 (2020) · Zbl 1454.83006 · doi:10.1007/JHEP09(2020)127 |
| [77] | Bern, Z.; Carrasco, JJM; Johansson, H., New Relations for Gauge-Theory Amplitudes, Phys. Rev. D, 78 (2008) · doi:10.1103/PhysRevD.78.085011 |
| [78] | Chakrabarti, A.; Tchrakian, DH, Antisymmetrized 2p forms generalizing curvature two forms and a corresponding p hierarchy of Schwarzschild type metrics in dimensions d > 2p + 1, Adv. Theor. Math. Phys., 3, 791 (1999) · Zbl 0997.83066 · doi:10.4310/ATMP.1999.v3.n4.a2 |
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