Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 83 tok/s
Gemini 2.5 Pro 34 tok/s Pro
GPT-5 Medium 24 tok/s Pro
GPT-5 High 21 tok/s Pro
GPT-4o 130 tok/s Pro
Kimi K2 207 tok/s Pro
GPT OSS 120B 460 tok/s Pro
Claude Sonnet 4.5 36 tok/s Pro
2000 character limit reached

What can abelian gauge theories teach us about kinematic algebras? (2401.10750v1)

Published 19 Jan 2024 in hep-th, gr-qc, and hep-ph

Abstract: The phenomenon of BCJ duality implies that gauge theories possess an abstract kinematic algebra, mirroring the non-abelian Lie algebra underlying the colour information. Although the nature of the kinematic algebra is known in certain cases, a full understanding is missing for arbitrary non-abelian gauge theories, such that one typically works outwards from well-known examples. In this paper, we pursue an orthogonal approach, and argue that simpler abelian gauge theories can be used as a testing ground for clarifying our understanding of kinematic algebras. We first describe how classes of abelian gauge fields are associated with well-defined subgroups of the diffeomorphism algebra. By considering certain special subgroups, we show that one may construct interacting theories, whose kinematic algebras are inherited from those already appearing in a related abelian theory. Known properties of (anti-)self-dual Yang-Mills theory arise in this way, but so do new generalisations, including self-dual electromagnetism coupled to scalar matter. Furthermore, a recently obtained non-abelian generalisation of the Navier-Stokes equation fits into a similar scheme, as does Chern-Simons theory. Our results provide useful input to further conceptual studies of kinematic algebras.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (63)
  1. Z. Bern, J. Carrasco, and H. Johansson, “New Relations for Gauge-Theory Amplitudes,” Phys.Rev. D78 (2008) 085011, 0805.3993.
  2. 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, 1004.0476.
  3. Z. Bern, T. Dennen, Y.-t. Huang, and M. Kiermaier, “Gravity as the Square of Gauge Theory,” Phys.Rev. D82 (2010) 065003, 1004.0693.
  4. H. Kawai, D. Lewellen, and S. Tye, “A Relation Between Tree Amplitudes of Closed and Open Strings,” Nucl.Phys. B269 (1986) 1.
  5. R. Monteiro, D. O’Connell, and C. D. White, “Black holes and the double copy,” JHEP 1412 (2014) 056, 1410.0239.
  6. A. Luna, R. Monteiro, D. O’Connell, and C. D. White, “The classical double copy for Taub-NUT spacetime,” Phys. Lett. B750 (2015) 272–277, 1507.01869.
  7. A. Luna, R. Monteiro, I. Nicholson, D. O’Connell, and C. D. White, “The double copy: Bremsstrahlung and accelerating black holes,” 1603.05737.
  8. A. Luna, R. Monteiro, I. Nicholson, A. Ochirov, D. O’Connell, N. Westerberg, and C. D. White, “Perturbative spacetimes from Yang-Mills theory,” JHEP 04 (2017) 069, 1611.07508.
  9. A. Luna, I. Nicholson, D. O’Connell, and C. D. White, “Inelastic Black Hole Scattering from Charged Scalar Amplitudes,” JHEP 03 (2018) 044, 1711.03901.
  10. N. Bahjat-Abbas, A. Luna, and C. D. White, “The Kerr-Schild double copy in curved spacetime,” JHEP 12 (2017) 004, 1710.01953.
  11. A. Luna, R. Monteiro, I. Nicholson, and D. O’Connell, “Type D Spacetimes and the Weyl Double Copy,” Class. Quant. Grav. 36 (2019) 065003, 1810.08183.
  12. W. D. Goldberger and A. K. Ridgway, “Radiation and the classical double copy for color charges,” Phys. Rev. D95 (2017), no. 12, 125010, 1611.03493.
  13. W. D. Goldberger, S. G. Prabhu, and J. O. Thompson, “Classical gluon and graviton radiation from the bi-adjoint scalar double copy,” Phys. Rev. D96 (2017), no. 6, 065009, 1705.09263.
  14. W. D. Goldberger, J. Li, and S. G. Prabhu, “Spinning particles, axion radiation, and the classical double copy,” Phys. Rev. D97 (2018), no. 10, 105018, 1712.09250.
  15. Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, “Chapter 2: An invitation to color-kinematics duality and the double copy,” J. Phys. A 55 (2022), no. 44, 443003, 2203.13013.
  16. T. Adamo, J. J. M. Carrasco, M. Carrillo-González, M. Chiodaroli, H. Elvang, H. Johansson, D. O’Connell, R. Roiban, and O. Schlotterer, “Snowmass White Paper: the Double Copy and its Applications,” in 2022 Snowmass Summer Study. 4, 2022. 2204.06547.
  17. D. A. Kosower, R. Monteiro, and D. O’Connell, “The SAGEX review on scattering amplitudes Chapter 14: Classical gravity from scattering amplitudes,” J. Phys. A 55 (2022), no. 44, 443015, 2203.13025.
  18. A. Buonanno, M. Khalil, D. O’Connell, R. Roiban, M. P. Solon, and M. Zeng, “Snowmass White Paper: Gravitational Waves and Scattering Amplitudes,” in Snowmass 2021. 4, 2022. 2204.05194.
  19. R. Monteiro and D. O’Connell, “The Kinematic Algebra From the Self-Dual Sector,” JHEP 1107 (2011) 007, 1105.2565.
  20. A. Parkes, “A Cubic action for selfdual Yang-Mills,” Phys.Lett. B286 (1992) 265–270, hep-th/9203074.
  21. J. Plebański, “Some solutions of complex Einstein equations,” J. Math. Phys. 16 (1975) 2395–2402.
  22. N. Bjerrum-Bohr, P. H. Damgaard, R. Monteiro, and D. O’Connell, “Algebras for Amplitudes,” JHEP 1206 (2012) 061, 1203.0944.
  23. E. Chacón, H. García-Compeán, A. Luna, R. Monteiro, and C. D. White, “New heavenly double copies,” JHEP 03 (2021) 247, 2008.09603.
  24. A. Lipstein and S. Nagy, “Self-Dual Gravity and Color-Kinematics Duality in AdS4,” Phys. Rev. Lett. 131 (2023), no. 8, 081501, 2304.07141.
  25. M. Ben-Shahar and H. Johansson, “Off-shell color-kinematics duality for Chern-Simons,” JHEP 08 (2022) 035, 2112.11452.
  26. S. Axelrod and I. M. Singer, “Chern-Simons perturbation theory,” in International Conference on Differential Geometric Methods in Theoretical Physics, pp. 3–45. 1991. hep-th/9110056.
  27. S. Axelrod and I. M. Singer, “Chern-Simons perturbation theory. II,” J. Diff. Geom. 39 (1994), no. 1, 173–213, hep-th/9304087.
  28. A. Edison, J. Mangan, and N. H. Pavao, “Revealing the Landscape of Globally Color-Dual Multi-loop Integrands,” 2309.16558.
  29. M. Reiterer, “A homotopy BV algebra for Yang-Mills and color-kinematics,” 1912.03110.
  30. L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, and M. Wolf, “Becchi-Rouet-Stora-Tyutin-Lagrangian Double Copy of Yang-Mills Theory,” Phys. Rev. Lett. 126 (2021), no. 19, 191601, 2007.13803.
  31. L. Borsten, H. Kim, B. Jurco, T. Macrelli, C. Saemann, and M. Wolf, “Double Copy from Homotopy Algebras,” Fortsch. Phys. 69 (2021), no. 8-9, 2100075, 2102.11390.
  32. L. Borsten, H. Kim, B. Jurco, T. Macrelli, C. Saemann, and M. Wolf, “Tree-level color–kinematics duality implies loop-level color–kinematics duality up to counterterms,” Nucl. Phys. B 989 (2023) 116144, 2108.03030.
  33. L. Borsten, H. Kim, B. Jurco, T. Macrelli, C. Saemann, and M. Wolf, “Colour-kinematics duality, double copy, and homotopy algebras,” PoS ICHEP2022 (11, 2022) 426, 2211.16405.
  34. L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, and M. Wolf, “Kinematic Lie Algebras From Twistor Spaces,” 2211.13261.
  35. L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, and M. Wolf, “Double Copy from Tensor Products of Metric BV■■{}^{\color[rgb]{.5,.5,.5}\blacksquare}start_FLOATSUPERSCRIPT ■ end_FLOATSUPERSCRIPT-algebras,” 2307.02563.
  36. F. Diaz-Jaramillo, O. Hohm, and J. Plefka, “Double field theory as the double copy of Yang-Mills theory,” Phys. Rev. D 105 (2022), no. 4, 045012, 2109.01153.
  37. R. Bonezzi, F. Diaz-Jaramillo, and O. Hohm, “The gauge structure of double field theory follows from Yang-Mills theory,” Phys. Rev. D 106 (2022), no. 2, 026004, 2203.07397.
  38. R. Bonezzi, C. Chiaffrino, F. Diaz-Jaramillo, and O. Hohm, “Gauge invariant double copy of Yang-Mills theory: The quartic theory,” Phys. Rev. D 107 (2023), no. 12, 126015, 2212.04513.
  39. R. Bonezzi, C. Chiaffrino, F. Diaz-Jaramillo, and O. Hohm, “Gravity = Yang-Mills,” 6, 2023. 2306.14788.
  40. I. A. Batalin and G. A. Vilkovisky, “Gauge Algebra and Quantization,” Phys. Lett. B 102 (1981) 27–31.
  41. I. A. Batalin and G. A. Vilkovisky, “Quantization of Gauge Theories with Linearly Dependent Generators,” Phys. Rev. D 28 (1983) 2567–2582. [Erratum: Phys.Rev.D 30, 508 (1984)].
  42. R. Bonezzi, F. Diaz-Jaramillo, and S. Nagy, “Gauge Independent Kinematic Algebra of Self-Dual Yang-Mills,” 2306.08558.
  43. S. Mizera, “Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes,” Phys. Rev. Lett. 124 (2020), no. 14, 141601, 1912.03397.
  44. C.-H. Fu and K. Krasnov, “Colour-Kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms,” JHEP 01 (2017) 075, 1603.02033.
  45. G. Chen, H. Johansson, F. Teng, and T. Wang, “On the kinematic algebra for BCJ numerators beyond the MHV sector,” JHEP 11 (2019) 055, 1906.10683.
  46. G. Chen, G. Lin, and C. Wen, “Kinematic Hopf algebra for amplitudes and form factors,” Phys. Rev. D 107 (2023), no. 8, L081701, 2208.05519.
  47. A. Brandhuber, G. Chen, H. Johansson, G. Travaglini, and C. Wen, “Kinematic Hopf Algebra for Bern-Carrasco-Johansson Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory,” Phys. Rev. Lett. 128 (2022), no. 12, 121601, 2111.15649.
  48. A. Brandhuber, G. R. Brown, G. Chen, J. Gowdy, G. Travaglini, and C. Wen, “Amplitudes, Hopf algebras and the colour-kinematics duality,” JHEP 12 (2022) 101, 2208.05886.
  49. C. R. Mafra and O. Schlotterer, “Multiparticle SYM equations of motion and pure spinor BRST blocks,” JHEP 07 (2014) 153, 1404.4986.
  50. C. R. Mafra and O. Schlotterer, “Berends-Giele recursions and the BCJ duality in superspace and components,” JHEP 03 (2016) 097, 1510.08846.
  51. K. Armstrong-Williams, C. D. White, and S. Wikeley, “Non-perturbative aspects of the self-dual double copy,” JHEP 08 (2022) 160, 2205.02136.
  52. C. Cheung and J. Mangan, “Scattering Amplitudes and the Navier-Stokes Equation,” 2010.15970.
  53. D. S. Berman, E. Chacón, A. Luna, and C. D. White, “The self-dual classical double copy, and the Eguchi-Hanson instanton,” 1809.04063.
  54. 2003.
  55. M. Campiglia and S. Nagy, “A double copy for asymptotic symmetries in the self-dual sector,” 2102.01680.
  56. S. Nagy and J. Peraza, “Radiative phase space extensions at all orders in r for self-dual Yang-Mills and gravity,” JHEP 02 (2023) 202, 2211.12991.
  57. Q. Liang and S. Nagy, “Convolutional double copy in (Anti) de Sitter space,” 2311.14319.
  58. R. Monteiro, R. Stark-Muchão, and S. Wikeley, “Anomaly and double copy in quantum self-dual Yang-Mills and gravity,” JHEP 09 (2023) 030, 2211.12407.
  59. G. Chalmers and W. Siegel, “The Selfdual sector of QCD amplitudes,” Phys. Rev. D 54 (1996) 7628–7633, hep-th/9606061.
  60. G. Chalmers and W. Siegel, “Simplifying algebra in Feynman graphs. Part 2. Spinor helicity from the space-cone,” Phys. Rev. D 59 (1999) 045013, hep-ph/9801220.
  61. 1995.
  62. M. M. Sheikh-Jabbari, V. Taghiloo, and M. H. Vahidinia, “Shallow Water Memory: Stokes and Darwin Drifts,” SciPost Phys. 15 (2023) 115, 2302.04912.
  63. D. Tong, “A gauge theory for shallow water,” SciPost Phys. 14 (2023), no. 5, 102, 2209.10574.
Citations (5)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets

This paper has been mentioned in 1 post and received 3 likes.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up to View