Coset space construction for the conformal group: Spontaneously
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 266-279 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We establish a mathematically rigorous way to construct effective theories resulting from the spontaneous breaking of conformal invariance. We show that the Nambu–Goldstone field corresponding to spontaneously broken generators of special conformal transformations is always a nondynamical degree of freedom. We prove that the developed approach and the standard approach including application of the inverse Higgs mechanism are equivalent.
Keywords: conformal field theory, inverse Higgs phenomenon, spontaneous space–time symmetry breaking.
Mots-clés : coset space technique
@article{TMF_2019_201_2_a7,
     author = {I. V. Kharuk},
     title = {Coset space construction for the~conformal group: {Spontaneously}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {266--279},
     year = {2019},
     volume = {201},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a7/}
}
TY  - JOUR
AU  - I. V. Kharuk
TI  - Coset space construction for the conformal group: Spontaneously
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2019
SP  - 266
EP  - 279
VL  - 201
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a7/
LA  - ru
ID  - TMF_2019_201_2_a7
ER  - 
%0 Journal Article
%A I. V. Kharuk
%T Coset space construction for the conformal group: Spontaneously
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2019
%P 266-279
%V 201
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a7/
%G ru
%F TMF_2019_201_2_a7
I. V. Kharuk. Coset space construction for the conformal group: Spontaneously. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 266-279. http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a7/

[1] A. Salam, J. A. Strathdee, “Nonlinear realizations. II. Conformal symmetry”, Phys. Rev., 184:5 (1969), 1760–1768 | DOI | MR

[2] P. W. Anderson, “Plasmons, gauge invariance, and mass”, Phys. Rev., 130:1 (1963), 439–442 | DOI | MR

[3] P. W. Higgs, “Broken symmetries, massless particles and gauge fields”, Phys. Lett., 12:2 (1964), 132–133 | DOI

[4] G. S. Guralnik, C. R. Hagen, T. W. Kibble, “Global conservation laws and massless particles”, Phys. Rev. Lett., 13:20 (1964), 585–587 | DOI

[5] C. J. Isham, A. Salam, J. A. Strathdee, “Spontaneous breakdown of conformal symmetry”, Phys. Lett. B, 31:5 (1970), 300–302 | DOI | MR

[6] D. V. Volkov, “Fenomenologicheskie lagranzhiany”, EChAYa, 4:1 (1973), 3–41 | MR

[7] I. Low, A. V. Manohar, “Spontaneously broken spacetime symmetries and Goldstone's theorem”, Phys. Rev. Lett., 88:10 (2002), 101602, 4 pp., arXiv: hep-th/0110285 | DOI

[8] E. A. Ivanov, V. I. Ogievetskii, “Obratnyi effekt Khiggsa v nelineinykh realizatsiyakh”, TMF, 25:2 (1975), 164–177 | DOI | MR

[9] A. Nicolis, R. Penco, F. Piazza, R. A. Rosen, “More on gapped Goldstones at finite density: more gapped Goldstones”, JHEP, 11 (2013), 055, 44 pp., arXiv: 1306.1240 | DOI

[10] H. Watanabe, H. Murayama, “Redundancies in Nambu–Goldstone bosons”, Phys. Rev. Lett., 110:18 (2013), 181601, 5 pp., arXiv: 1302.4800 | DOI

[11] K. Hinterbichler, A. Joyce, J. Khoury, “Non-linear realizations of conformal symmetry and effective field theory for the pseudo-conformal universe”, JCAP, 06 (2012), 043, arXiv: 1202.6056 | DOI

[12] I. Kharuk, “Coset space construction for the conformal group”, Phys. Rev. D, 98 (2018), 025006, 10 pp., arXiv: 1711.03411 | DOI | MR

[13] G. W. Mackey, Induced Representations of Groups and Quantum Mechanics, Editore Boringhieri, Turin, 1968 | MR

[14] R. Hermann, Lie Groups for Physicists, v. 5, W. A. Benjamin, New York, 1966 | MR

[15] T. Ortín, Gravity and Strings, Cambridge Univ. Press, Cambridge, 2015 | MR

[16] A. Wehner, “Symmetric spaces with conformal symmetry”, arXiv: hep-th/0107008

[17] E. A. Ivanov, J. Niederle, “Gauge formulation of gravitation theories. II. The special conformal case”, Phys. Rev. D, 25:4 (1982), 988–994 | DOI | MR

[18] V. I. Ogievetsky, “Nonlinear realization of internal and space-time symmetries”, New Developments in Relativistic Quantum Field Theory (Karpacz, February 19 – March 4, 1973), v. I, Universitatis Wratislaviensis, Poland, 1974, 117–141 | MR

[19] E. A. Ivanov, V. I. Ogievetsky, “Gauge theories as theories of spontaneous breakdown”, Lett. Math. Phys., 1:4 (1976), 309–313 | DOI | MR

[20] G. Goon, A. Joyce, M. Trodden, “Spontaneously broken gauge theories and the coset construction”, Phys. Rev. D, 90:2 (2014), 025022, 14 pp., arXiv: 1405.5532 | DOI

[21] S. Weinberg, The Quantum Theory of Fields, v. 2, Modern Applications, Cambridge Univ. Press, Cambridge, 2013 | DOI | MR

[22] C. G. Callan Jr., S. R. Coleman, R. Jackiw, “A new improved energy-momentum tensor”, Ann. Phys., 59:1 (1970), 42–73 | DOI | MR

[23] S. El-Showk, Y. Nakayama, S. Rychkov, “What Maxwell theory in $d\neq 4$ teaches us about scale and conformal invariance”, Nucl. Phys. B, 848:3 (2011), 578–593, arXiv: 1101.5385 | DOI | MR

[24] S. Weinberg, The Quantum Theory of Fields, v. 3, Supersymmetry, Cambridge Univ. Press, Cambridge, 2013 | DOI | MR

[25] S. R. Coleman, J. Mandula, “All possible symmetries of the $S$ matrix”, Phys. Rev., 159:5 (1967), 1251–1256 | DOI

[26] E. A. Ivanov, J. Niederle, “Gauge formulation of gravitation theories. I. The Poincaré, de Sitter, and conformal cases”, Phys. Rev. D, 25:4 (1982), 976–987 | DOI | MR

[27] G. Goon, K. Hinterbichler, A. Joyce, M. Trodden, “Einstein gravity, massive gravity, multi-gravity and nonlinear realizations”, JHEP, 07 (2015), 101, 31 pp., arXiv: 1412.6098 | DOI | MR