Geodesic
Deformed $w_{1+\infty}$ Algebras in the Celestial CFT
Symmetry, integrability and geometry: methods and applications, Tome 19 (2023) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 $W_{1+\infty}$.
Keywords: celestial holography, CFT, OPE, algebra; current, $w$-infinity, commutator, Jacobi identity.
Mots-clés : gluon, graviton 
@article{SIGMA_2023_19_a43,
     author = {Jorge Mago and Lecheng Ren and Akshay Yelleshpur Srikant and Anastasia Volovich},
     title = {Deformed $w_{1+\infty}$ {Algebras} in the {Celestial} {CFT}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2023},
     volume = {19},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a43/}
}
TY  - JOUR
AU  - Jorge Mago
AU  - Lecheng Ren
AU  - Akshay Yelleshpur Srikant
AU  - Anastasia Volovich
TI  - Deformed $w_{1+\infty}$ Algebras in the Celestial CFT
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2023
VL  - 19
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a43/
LA  - en
ID  - SIGMA_2023_19_a43
ER  - 
%0 Journal Article
%A Jorge Mago
%A Lecheng Ren
%A Akshay Yelleshpur Srikant
%A Anastasia Volovich
%T Deformed $w_{1+\infty}$ Algebras in the Celestial CFT
%J Symmetry, integrability and geometry: methods and applications
%D 2023
%V 19
%U http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a43/
%G en
%F SIGMA_2023_19_a43
Jorge Mago; Lecheng Ren; Akshay Yelleshpur Srikant; Anastasia Volovich. Deformed $w_{1+\infty}$ Algebras in the Celestial CFT. Symmetry, integrability and geometry: methods and applications, Tome 19 (2023). http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a43/

[1] Adamo T., Mason L., Sharma A., “Celestial amplitudes and conformal soft theorems”, Classical Quantum Gravity, 36 (2019), 205018, 22 pp., arXiv: 1905.09224 | DOI | MR | Zbl

[2] Adamo T., Mason L., Sharma A., “Celestial $w_{1+\infty}$ symmetries from twistor space”, SIGMA, 18 (2022), 016, 23 pp., arXiv: 2110.06066 | DOI | MR | Zbl

[3] Ahn C., “Towards a supersymmetric $w_{1+\infty}$ symmetry in the celestial conformal field theory”, Phys. Rev. D, 105 (2022), 086028, 13 pp., arXiv: 2111.04268 | DOI | MR

[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), 47, 27 pp., arXiv: 2109.00997 | DOI

[5] Bakas I., “The large-$N$ limit of extended conformal symmetries”, Phys. Lett. B, 228 (1989), 57–63 | DOI | MR

[6] Ball A., “Celestial locality and the Jacobi identity”, J. High Energy Phys., 2023:1 (2023), 146, 16 pp., arXiv: 2211.09151 | DOI | MR

[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 | DOI | MR

[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 | DOI

[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 pp., arXiv: 1405.1015 | DOI

[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 pp., arXiv: hep-ph/9903516 | DOI

[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 | DOI

[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 | DOI | MR

[13] Bu W., Heuveline S., Skinner D., “Moyal deformations, $W_{1+\infty}$ and celestial holography”, J. High Energy Phys., 2022:12 (2022), 011, 20 pp., arXiv: 2208.13750 | DOI | MR

[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., 2014:8 (2014), 077, 5 pp., arXiv: 1404.5551 | DOI | MR

[16] Chalmers G., Siegel W., “Self-dual sector of QCD amplitudes”, Phys. Rev. D, 54 (1996), 7628–7633, arXiv: hep-th/9606061 | DOI

[17] Dixon L.J., Glover E.W.N., Khoze V.V., “MHV rules for Higgs plus multi-gluon amplitudes”, J. High Energy Phys., 2004:12 (2004), 015, 35 pp., arXiv: hep-th/0411092 | DOI | MR

[18] Donnay L., Puhm A., Strominger A., “Conformally soft photons and gravitons”, J. High Energy Phys., 2019:1 (2019), 184, 22 pp., arXiv: 1810.05219 | DOI | MR | Zbl

[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 pp., arXiv: 1611.07534 | DOI

[21] Fairlie D.B., Nuyts J., “Deformations and renormalisations of $W_\infty$”, Comm. Math. Phys., 134 (1990), 413–419 | DOI | MR | Zbl

[22] Fan W., Fotopoulos A., Taylor T.R., “Soft limits of Yang–Mills amplitudes and conformal correlators”, J. High Energy Phys., 2019:5 (2019), 121, 15 pp., arXiv: 1903.01676 | DOI | MR

[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., 2021:11 (2021), 152, 17 pp., arXiv: 2103.03961 | DOI | MR

[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 pp., arXiv: 1801.05528 | DOI

[26] He S., Huang Y.-T., Wen C., “Loop corrections to soft theorems in gauge theories and gravity”, J. High Energy Phys., 2014:12 (2014), 115, 21 pp., arXiv: 1405.1410 | DOI | MR

[27] Himwich E., Pate M., Singh K., “Celestial operator product expansions and $w_{1+\infty}$ symmetry for all spins”, J. High Energy Phys., 2022:1 (2022), 080, 28 pp., arXiv: 2108.07763 | DOI | MR

[28] Jiang H., “Celestial OPEs and $w_{1+\infty}$ algebra from worldsheet in string theory”, J. High Energy Phys., 2022:1 (2022), 101, 57 pp., arXiv: 2110.04255 | DOI | MR

[29] Jiang H., “Holographic chiral algebra: supersymmetry, infinite Ward identities, and EFTs”, J. High Energy Phys., 2022:1 (2022), 113, 38 pp., arXiv: 2108.08799 | DOI | MR

[30] Klose T., McLoughlin T., Nandan D., Plefka J., Travaglini G., “Double-soft limits of gluons and gravitons”, J. High Energy Phys., 2015:7 (2015), 135, 30 pp., arXiv: 1504.05558 | DOI | MR | Zbl

[31] Li Z.-Z., Lin H.-H., Zhang S.-Q., “Infinite soft theorems from gauge symmetry”, Phys. Rev. D, 98 (2018), 045004, 8 pp., arXiv: 1802.03148 | DOI | MR

[32] Mahlon G., “Multigluon helicity amplitudes involving a quark loop”, Phys. Rev. D, 49 (1994), 4438–4453, arXiv: hep-ph/9312276 | DOI

[33] Nandan D., Schreiber A., Volovich A., Zlotnikov M., “Celestial amplitudes: conformal partial waves and soft limits”, J. High Energy Phys., 2019:10 (2019), 018, 13 pp., arXiv: 1904.10940 | DOI | MR

[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 | DOI | MR

[35] Pasterski S., “Lectures on celestial amplitudes”, Eur. Phys. J. C, 81 (2021), 1062, 24 pp., arXiv: 2108.04801 | DOI

[36] Pasterski S., Shao S.-H., “Conformal basis for flat space amplitudes”, Phys. Rev. D, 96 (2017), 065022, 17 pp., arXiv: 1705.01027 | DOI | MR

[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 pp., arXiv: 1701.00049 | DOI | MR

[38] Pasterski S., Shao S.-H., Strominger A., “Gluon amplitudes as $2d$ conformal correlators”, Phys. Rev. D, 96 (2017), 085006, 13 pp., arXiv: 1706.03917 | DOI | MR

[39] Pate M., Raclariu A.-M., Strominger A., “Conformally soft theorem in gauge theory”, Phys. Rev. D, 100 (2019), 085017, 10 pp., arXiv: 1904.10831 | DOI | MR

[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 pp., arXiv: 1910.07424 | DOI | MR

[41] Pope C.N., “Lectures on W algebras and W gravity”, Summer School in High-energy Physics and Cosmology (Trieste, Italy, 1991), v. 1–2, 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 | DOI | MR

[43] Pope C.N., Shen X., Romans L.J., “$W_\infty$ and the Racah–Wigner algebra”, Nuclear Phys. B, 339 (1990), 191–221 | DOI | MR

[44] Pope C.N., Shen X., Xu K.W., Yuan K., “${\rm SL}(\infty,R)$ symmetry of quantum $W_\infty$ gravity”, Nuclear Phys. B, 376 (1992), 52–74, arXiv: hep-th/9201023 | DOI | MR

[45] Puhm A., “Conformally soft theorem in gravity”, J. High Energy Phys., 2020:9 (2020), 130, 14 pp., arXiv: 1905.09799 | DOI | MR

[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 | DOI | MR | Zbl

[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 pp., arXiv: 2105.14346 | DOI | MR

[49] Volovich A., Wen C., Zlotnikov M., “Double soft theorems in gauge and string theories”, J. High Energy Phys., 2015:7 (2015), 095, 25 pp., arXiv: 1504.05559 | DOI | MR

[50] Weinberg S., “Infrared photons and gravitons”, Phys. Rev., 140 (1965), B516–B524 | DOI | MR