Geodesic
The ring of physical states in the $M(2,3)$ minimal Liouville gravity
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 1, pp. 119-140 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the $M(2,3)$ minimal Liouville gravity, whose state space in the gravity sector is realized as irreducible modules of the Virasoro algebra. We present a recursive construction for BRST cohomology classes based on using an explicit form of singular vectors in irreducible modules of the Virasoro algebra. We find a certain algebra acting on the BRST cohomology space and use this algebra to find the operator algebra of physical states.
Keywords: conformal field theory, Liouville gravity, BRST cohomology. 
@article{TMF_2010_164_1_a7,
     author = {O. V. Alekseev and M. A. Bershtein},
     title = {The~ring of physical states in the~$M(2,3)$ minimal {Liouville} gravity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {119--140},
     year = {2010},
     volume = {164},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_164_1_a7/}
}
TY  - JOUR
AU  - O. V. Alekseev
AU  - M. A. Bershtein
TI  - The ring of physical states in the $M(2,3)$ minimal Liouville gravity
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2010
SP  - 119
EP  - 140
VL  - 164
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2010_164_1_a7/
LA  - ru
ID  - TMF_2010_164_1_a7
ER  - 
%0 Journal Article
%A O. V. Alekseev
%A M. A. Bershtein
%T The ring of physical states in the $M(2,3)$ minimal Liouville gravity
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2010
%P 119-140
%V 164
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2010_164_1_a7/
%G ru
%F TMF_2010_164_1_a7
O. V. Alekseev; M. A. Bershtein. The ring of physical states in the $M(2,3)$ minimal Liouville gravity. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 1, pp. 119-140. http://geodesic.mathdoc.fr/item/TMF_2010_164_1_a7/

[1] A. Polyakov, Phys. Lett. B, 103:3 (1981), 207–210 | DOI | MR

[2] J. Distler, H. Kawai, Nucl. Phys. B, 321:2 (1989), 509–527 ; F. David, Modern Phys. Lett. A, 3:17 (1988), 1651–1656 | DOI | MR | DOI | MR

[3] A. A. Belavin, A. M. Polyakov, A. B. Zamolodchikov, Nucl. Phys. B, 241:2 (1984), 333–380 | DOI | MR | Zbl

[4] Al. B. Zamolodchikov, TMF, 142:2 (2005), 218–234 ; arXiv: hep-th/0505063 | DOI | MR | Zbl

[5] A. A. Belavin, Al. B. Zamolodchikov, TMF, 147:3 (2006), 339–371 ; Polyakov's string: twenty five years after, arXiv: hep-th/0510214 | DOI | MR | Zbl

[6] B. H. Lian, G. J. Zuckerman, Phys. Lett. B, 254:3–4 (1991), 417–423 | DOI | MR | Zbl

[7] B. Feĭgin, D. Fuchs, “Representations of the Virasoro algebra”, Representations of Lie Groups and Related Topics, Adv. Stud. Contemp. Math., 7, eds. A. M. Vershik, D. P. Zhelobenko, Gordon and Breach, New York, 1990, 465–554 | MR | Zbl

[8] H. Kanno, M. Sarmadi, Internat. J. Modern Phys. A, 9:1 (1994), 39–56 ; arXiv: hep-th/9207078 | DOI | MR | Zbl

[9] A. Zamolodchikov, Al. Zamolodchikov, Nucl. Phys. B, 477:2 (1996), 577–605 ; arXiv: hep-th/9506136 | DOI | MR | Zbl

[10] C. Imbimbo, S. Mahapatra, S. Mukhi, Nucl. Phys. B, 375:2 (1992), 399–420 | DOI | MR

[11] B. L. Feĭgin, D. B. Fuchs, “Verma modules over the Virasoro algebra”, Topology, Lecture Notes in Math., 1060, eds. L. D. Faddeev, A. A. Mal'cev, Springer, Berlin, 1984, 230–245 | DOI | MR | Zbl

[12] E. Frenkel, Phys. Lett. B, 286:1–2 (1992), 71–77 | DOI | MR

[13] S. Govindarajan, T. Jayaraman, V. John, P. Majumdar, Modern Phys. Lett. A, 7:12 (1992), 1063–1077 ; arXiv: hep-th/9112033 | DOI | MR | Zbl

[14] S. Govindarajan, T. Jayaraman, V. John, Nucl. Phys. B, 402:1–2 (1993), 118–136 ; arXiv: hep-th/9207109 | DOI | MR | Zbl

[15] I. B. Frenkel, H. Garland, G. J. Zuckerman, Proc. Nat. Acad. Sci. USA, 83:22 (1986), 8442–8446 | DOI | MR | Zbl

[16] L. V. Goncharova, Funkts. analiz i ego pril., 7:2 (1973), 6–14 | DOI | MR | Zbl

[17] M. Bauer, P. Di Francesco, C. Itzykson, J.-B. Zuber, Nucl. Phys. B, 362:3 (1991), 515–562 | DOI | MR | Zbl

[18] H. Dorn, H.-J. Otto, Phys. Lett. B, 291:1–2 (1992), 39–43 ; arXiv: ; Nucl. Phys. B, 429:2 (1994), 375–388 ; arXiv: hep-th/9206053hep-th/9403141 | DOI | MR | DOI | MR | Zbl

[19] F. Griffits, Dzh. Kharris, Printsipy algebraicheskoi geometrii, Mir, M., 1982 | MR | MR | Zbl

[20] B. H. Lian, G. J. Zuckerman, Comm. Math. Phys., 154:3 (1993), 613–646 ; arXiv: hep-th/9211072 | DOI | MR | Zbl