- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Constructing conformal double field theory through a double copy map

Eric Lescano1,* and Jesús A. Rodríguez2,†

  • *Contact author: eric.lescano@uwr.edu.pl
  • †Contact author: jarodriguez@df.uba.ar
PDF

Phys. Rev. D 112, 026004 – Published 1 July, 2025

DOI: https://doi.org/10.1103/vxch-63hj

Abstract

We follow the classical double copy (DC) procedure that links Yang-Mills and double field theory (DFT), and apply it on a four-derivative gauge theory which is known to be related to Weyl gravity at the level of the amplitudes. We obtain a perturbative T-duality invariant theory on a double geometry, or conformal double field theory (CDFT), incorporating Weyl gravity plus b-field and dilaton contributions at quadratic order, without the need to impose a gauge-fixing condition. We also extend the formulation to cubic order for the case of vanishing generalized dilaton, which still incorporates Weyl gravity when □hμν=h=0. CDFT, together with ordinary DFT, are examples of T-duality invariant theories constructed through classical DC maps, revealing a promising and deep connection between gauge theories and T-duality invariant models.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (41)

  1. C. Hull and B. Zwiebach, Double field theory, J. High Energy Phys. 09 (2009) 099.
  2. O. Hohm, C. Hull, and B. Zwiebach, Generalized metric formulation of double field theory, J. High Energy Phys. 08 (2010) 008.
  3. Z. Bern, J. J. M. Carrasco, and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78, 085011 (2008).
  4. Z. Bern, J. J. M. Carrasco, and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett. 105, 061602 (2010).
  5. Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, The duality between color and kinematics and its applications, J. Phys. A 57, 333002 (2024).
  6. T. Adamo, J. J. M. Carrasco, M. Carrillo-Gonzalez, M. Chiodaroli, H. Elvang, H. Johansson, D. O’Connell, R. Roiban, and O. Schlotterer, Snowmass White Paper: The double copy and its applications, arXiv:2204.06547.
  7. H. Kawai, D. C. Lewellen, and S. H. H. Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys. B269, 1 (1986).
  8. R. Monteiro, D. O’Connell, and C. D. White, Black holes and the double copy, J. High Energy Phys. 12 (2014) 056.
  9. A. Luna, R. Monteiro, I. Nicholson, A. Ochirov, D. O’Connell, N. Westerberg, and C. D. White, Perturbative spacetimes from Yang-Mills theory, J. High Energy Phys. 04 (2017) 069.
  10. W. D. Goldberger and A. K. Ridgway, Bound states and the classical double copy, Phys. Rev. D 97, 085019 (2018).
  11. J. Plefka, J. Steinhoff, and W. Wormsbecher, Effective action of dilaton gravity as the classical double copy of Yang-Mills theory, Phys. Rev. D 99, 024021 (2019).
  12. N. E. J. Bjerrum-Bohr, P. H. Damgaard, G. Festuccia, L. Planté, and P. Vanhove, General relativity from scattering amplitudes, Phys. Rev. Lett. 121, 171601 (2018).
  13. A. Brandhuber, G. Chen, G. Travaglini, and C. Wen, Classical gravitational scattering from a gauge-invariant double copy, J. High Energy Phys. 10 (2021) 118.
  14. 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, 121601 (2022).
  15. F. Diaz-Jaramillo, O. Hohm, and J. Plefka, Double field theory as the double copy of Yang-Mills theory, Phys. Rev. D 105, 045012 (2022).
  16. R. Bonezzi, F. Diaz-Jaramillo, and O. Hohm, The gauge structure of double field theory follows from Yang-Mills theory, Phys. Rev. D 106, 026004 (2022).
  17. 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, 126015 (2023).
  18. R. Bonezzi, C. Chiaffrino, F. Diaz-Jaramillo, and O. Hohm, Weakly constrained double field theory as the double copy of Yang-Mills theory, Phys. Rev. D 109, 066020 (2024).
  19. E. Lescano, G. Menezes, and J. A. Rodriguez, Aspects of conformal gravity and double field theory from a double copy map, Phys. Rev. D 108, 126017 (2023).
  20. H. Johansson and J. Nohle, Conformal gravity from gauge theory, arXiv:1707.02965.
  21. H. Johansson, G. Mogull, and F. Teng, Unraveling conformal gravity amplitudes, J. High Energy Phys. 09 (2018) 080.
  22. T. Azevedo, R. L. Jusinskas, and M. Lize, Bosonic sectorized strings and the (DF)2 theory, J. High Energy Phys. 01 (2020) 082.
  23. G. Menezes, Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity, J. High Energy Phys. 03 (2022) 074.
  24. G. Menezes, Leading singularities in higher-derivative Yang–Mills theory and quadratic gravity, Universe 8, 326 (2022).
  25. K. Lee, Kerr-Schild double field theory and classical double copy, J. High Energy Phys. 10 (2018) 027.
  26. W. Cho and K. Lee, Heterotic Kerr-Schild double field theory and classical double copy, J. High Energy Phys. 07 (2019) 030.
  27. E. Lescano and A. Rodríguez, N=1 supersymmetric double field theory and the generalized Kerr-Schild Ansatz, J. High Energy Phys. 10 (2020) 148.
  28. E. Lescano and A. Rodríguez, Higher-derivative heterotic double field theory and classical double copy, J. High Energy Phys. 07 (2021) 072.
  29. S. Angus, K. Cho, and K. Lee, The classical double copy for half-maximal supergravities and T-duality, J. High Energy Phys. 10 (2021) 211.
  30. K. Kim, K. Lee, R. Monteiro, I. Nicholson, and D. P. Veiga, The classical double copy of a point charge, J. High Energy Phys. 02 (2020) 046.
  31. E. Lescano and S. Roychowdhury, Heterotic Kerr-Schild double field theory and its double Yang-Mills formulation, J. High Energy Phys. 04 (2022) 090.
  32. G. Aldazabal, D. Marques, and C. Nuñez, Double field theory: A pedagogical review, Classical Quantum Gravity 30, 163001 (2013).
  33. O. Hohm, D. Lust, and B. Zwiebach, The spacetime of double field theory: Review, remarks, and outlook, Fortschr. Phys. 61, 926 (2013).
  34. D. S. Berman and D. C. Thompson, Duality symmetric string and M-theory, Phys. Rep. 566, 1 (2014).
  35. E. Lescano, α′–corrections and their double formulation, J. Phys. A 55, 053002 (2022).
  36. K. Peeters, Introducing Cadabra: A symbolic computer algebra system for field theory problems, arXiv:hep-th/0701238.
  37. D. Marques and C. Nuñez, T-duality and α′-corrections, J. High Energy Phys. 10 (2015) 084.
  38. W. H. Baron, J. J. Fernandez-Melgarejo, D. Marques, and C. Nunez, The odd story of α′-corrections, J. High Energy Phys. 04 (2017) 078.
  39. E. Lescano, C. A. Núñez, and J. A. Rodríguez, Supersymmetry, T-duality and heterotic α′-corrections, J. High Energy Phys. 07 (2021) 092.
  40. O. Hohm, W. Siegel, and B. Zwiebach, Doubled α′-geometry, J. High Energy Phys. 02 (2014) 065.
  41. E. Lescano and D. Marques, Second order higher-derivative corrections in double field theory, J. High Energy Phys. 06 (2017) 104.

Outline

Information

Phys. Rev. D 112, 026004– Published 1 July, 2025
  • Received 22 January 2025
  • Accepted 22 May 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation