Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 044, 18 pages      arXiv:2111.11356      https://doi.org/10.3842/SIGMA.2023.044

Deformed $w_{1+\infty}$ Algebras in the Celestial CFT

Jorge Mago, Lecheng Ren, Akshay Yelleshpur Srikant and Anastasia Volovich
Department of Physics, Brown University, Providence, RI 02912, USA

Received January 19, 2023, in final form May 22, 2023; Published online July 04, 2023

Abstract
We compute the modification of the $w_{1+\infty}$ algebra of soft graviton, gluon and scalar currents in the celestial CFT due to non-minimal couplings. We find that the Jacobi identity is satisfied only when the spectrum and couplings of the theory obey certain constraints. We comment on the similarities and essential differences of this algebra to $W_{1+\infty}$.

Key words: celestial holography; CFT; OPE; algebra; current; gluon; graviton; $w$-infinity; commutator; Jacobi identity.

pdf (480 kb)   tex (28 kb)  

References

  1. Adamo T., Mason L., Sharma A., Celestial amplitudes and conformal soft theorems, Classical Quantum Gravity 36 (2019), 205018, 22 pages, arXiv:1905.09224.
  2. Adamo T., Mason L., Sharma A., Celestial $w_{1+\infty}$ symmetries from twistor space, SIGMA 18 (2022), 016, 23 pages, arXiv:2110.06066.
  3. Ahn C., Towards a supersymmetric $w_{1+\infty}$ symmetry in the celestial conformal field theory, Phys. Rev. D 105 (2022), 086028, 13 pages, arXiv:2111.04268.
  4. Aneesh P.B., Compère G., de Gioia L.P., Mol I., Swidler B., Celestial holography: Lectures on asymptotic symmetries, SciPost Phys. Lect. Notes 2022 (2022), article no. 47, 27 pages, arXiv:2109.00997.
  5. Bakas I., The large-$N$ limit of extended conformal symmetries, Phys. Lett. B 228 (1989), 57-63.
  6. Ball A., Celestial locality and the Jacobi identity, J. High Energy Phys. 2023 (2023), no. 1, 146, 16 pages, arXiv:2211.09151.
  7. Bergshoeff E., Howe P.S., Pope C.N., Sezgin E., Shen X., Stelle K.S., Quantisation deforms $w_\infty$ to $W_\infty$ gravity, Nuclear Phys. B 363 (1991), 163-184.
  8. Bern Z., Chalmers G., Dixon L., Kosower D.A., One-loop $n$-gluon amplitudes with maximal helicity violation via collinear limits, Phys. Rev. Lett. 72 (1994), 2134-3237, arXiv:hep-ph/9312333.
  9. Bern Z., Davies S., Nohle J., On loop corrections to subleading soft behavior of gluons and gravitons, Phys. Rev. D 90 (2014), 085015, 10 pages, arXiv:1405.1015.
  10. Bern Z., Del Duca V., Kilgore W.B., Schmidt C.R., Infrared behavior of one-loop QCD amplitudes at next-to-next-to-leading order, Phys. Rev. D 60 (1999), 116001, 25 pages, arXiv:hep-ph/9903516.
  11. Bern Z., Del Duca V., Schmidt C.R., The infrared behavior of one-loop gluon amplitudes at next-to-next-to-leading order, Phys. Lett. B 445 (1998), 168-177, arXiv:hep-ph/9810409.
  12. Bern Z., Dixon L., Perelstein M., Rozowsky J.S., One-loop $n$-point helicity amplitudes in (self-dual) gravity, Phys. Lett. B 444 (1998), 273-283, arXiv:hep-th/9809160.
  13. Bu W., Heuveline S., Skinner D., Moyal deformations, $W_{1+\infty}$ and celestial holography, J. High Energy Phys. 2022 (2022), no. 12, 011, 20 pages, arXiv:2208.13750.
  14. Cachazo F., Yuan E.Y., Are soft theorems renormalized?, arXiv:1405.3413.
  15. Casali E., Soft sub-leading divergences in Yang-Mills amplitudes, J. High Energy Phys. 2014 (2014), no. 8, 077, 5 pages, arXiv:1404.5551.
  16. Chalmers G., Siegel W., Self-dual sector of QCD amplitudes, Phys. Rev. D 54 (1996), 7628-7633, arXiv:hep-th/9606061.
  17. Dixon L.J., Glover E.W.N., Khoze V.V., MHV rules for Higgs plus multi-gluon amplitudes, J. High Energy Phys. 2004 (2004), no. 12, 015, 35 pages, arXiv:hep-th/0411092.
  18. Donnay L., Puhm A., Strominger A., Conformally soft photons and gravitons, J. High Energy Phys. 2019 (2019), no. 1, 184, 22 pages, arXiv:1810.05219.
  19. Elvang H., Huang Y.-T., Scattering amplitudes, arXiv:1308.1697.
  20. Elvang H., Jones C.R.T., Naculich S.G., Soft photon and graviton theorems in effective field theory, Phys. Rev. Lett. 118 (2017), 231601, 6 pages, arXiv:1611.07534.
  21. Fairlie D.B., Nuyts J., Deformations and renormalisations of $W_\infty$, Comm. Math. Phys. 134 (1990), 413-419.
  22. Fan W., Fotopoulos A., Taylor T.R., Soft limits of Yang-Mills amplitudes and conformal correlators, J. High Energy Phys. 2019 (2019), no. 5, 121, 15 pages, arXiv:1903.01676.
  23. Guevara A., Notes on conformal soft theorems and recursion relations in gravity, arXiv:1906.07810.
  24. Guevara A., Himwich E., Pate M., Strominger A., Holographic symmetry algebras for gauge theory and gravity, J. High Energy Phys. 2021 (2021), no. 11, 152, 17 pages, arXiv:2103.03961.
  25. Hamada Y., Shiu G., Infinite set of soft theorems in gauge-gravity theories as Ward-Takahashi identities, Phys. Rev. Lett. 120 (2018), 201601, 6 pages, arXiv:1801.05528.
  26. He S., Huang Y.-T., Wen C., Loop corrections to soft theorems in gauge theories and gravity, J. High Energy Phys. 2014 (2014), no. 12, 115, 21 pages, arXiv:1405.1410.
  27. Himwich E., Pate M., Singh K., Celestial operator product expansions and $w_{1+\infty}$ symmetry for all spins, J. High Energy Phys. 2022 (2022), no. 1, 080, 28 pages, arXiv:2108.07763.
  28. Jiang H., Celestial OPEs and $w_{1+\infty}$ algebra from worldsheet in string theory, J. High Energy Phys. 2022 (2022), no. 1, 101, 57 pages, arXiv:2110.04255.
  29. Jiang H., Holographic chiral algebra: supersymmetry, infinite Ward identities, and EFTs, J. High Energy Phys. 2022 (2022), no. 1, 113, 38 pages, arXiv:2108.08799.
  30. Klose T., McLoughlin T., Nandan D., Plefka J., Travaglini G., Double-soft limits of gluons and gravitons, J. High Energy Phys. 2015 (2015), no. 7, 135, 30 pages, arXiv:1504.05558.
  31. Li Z.-Z., Lin H.-H., Zhang S.-Q., Infinite soft theorems from gauge symmetry, Phys. Rev. D 98 (2018), 045004, 8 pages, arXiv:1802.03148.
  32. Mahlon G., Multigluon helicity amplitudes involving a quark loop, Phys. Rev. D 49 (1994), 4438-4453, arXiv:hep-ph/9312276.
  33. Nandan D., Schreiber A., Volovich A., Zlotnikov M., Celestial amplitudes: conformal partial waves and soft limits, J. High Energy Phys. 2019 (2019), no. 10, 018, 13 pages, arXiv:1904.10940.
  34. Odake S., Sano T., $W_{1+\infty}$ and super-$W_\infty$ algebras with ${\rm SU}(N)$ symmetry, Phys. Lett. B 258 (1991), 369-374.
  35. Pasterski S., Lectures on celestial amplitudes, Eur. Phys. J. C 81 (2021), 1062, 24 pages, arXiv:2108.04801.
  36. Pasterski S., Shao S.-H., Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017), 065022, 17 pages, arXiv:1705.01027.
  37. Pasterski S., Shao S.-H., Strominger A., Flat space amplitudes and conformal symmetry of the celestial sphere, Phys. Rev. D 96 (2017), 065026, 7 pages, arXiv:1701.00049.
  38. Pasterski S., Shao S.-H., Strominger A., Gluon amplitudes as $2d$ conformal correlators, Phys. Rev. D 96 (2017), 085006, 13 pages, arXiv:1706.03917.
  39. Pate M., Raclariu A.-M., Strominger A., Conformally soft theorem in gauge theory, Phys. Rev. D 100 (2019), 085017, 10 pages, arXiv:1904.10831.
  40. Pate M., Raclariu A.-M., Strominger A., Yuan E.Y., Celestial operator products of gluons and gravitons, Rev. Math. Phys. 33 (2021), 2140003, 28 pages, arXiv:1910.07424.
  41. Pope C.N., Lectures on W algebras and W gravity, in Summer School in High-energy Physics and Cosmology, Vols. 1-2, Trieste, Italy, 1991, 827-867, arXiv:hep-th/9112076.
  42. Pope C.N., Romans L.J., Shen X., The complete structure of $W_\infty$, Phys. Lett. B 236 (1990), 173-178.
  43. Pope C.N., Shen X., Romans L.J., $W_\infty$ and the Racah-Wigner algebra, Nuclear Phys. B 339 (1990), 191-221.
  44. Pope C.N., Shen X., Xu K.W., Yuan K., ${\rm SL}(\infty,{\bf R})$ symmetry of quantum $W_\infty$ gravity, Nuclear Phys. B 376 (1992), 52-74, arXiv:hep-th/9201023.
  45. Puhm A., Conformally soft theorem in gravity, J. High Energy Phys. 2020 (2020), no. 9, 130, 14 pages, arXiv:1905.09799.
  46. Raclariu A.-M., Lectures on celestial holography, arXiv:2107.02075.
  47. Strominger A., Lectures on the infrared structure of gravity and gauge theory, Princeton University Press, Princeton, NJ, 2018, arXiv:1703.05448.
  48. Strominger A., $w_{1+\infty}$ algebra and the celestial sphere: infinite towers of soft graviton, photon, and gluon symmetries, Phys. Rev. Lett. 127 (2021), 221601, 5 pages, arXiv:2105.14346.
  49. Volovich A., Wen C., Zlotnikov M., Double soft theorems in gauge and string theories, J. High Energy Phys. 2015 (2015), no. 7, 095, 25 pages, arXiv:1504.05559.
  50. Weinberg S., Infrared photons and gravitons, Phys. Rev. 140 (1965), B516-B524.

Previous article  Next article  Contents of Volume 19 (2023)