Geodesic
$d\le 1\cup d\ge 25$ and constrained KP hierarchy from BRST invariance in the $c\ne 3$ topological algebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 2, pp. 239-250 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The BRST invariance condition in a highest-weight representation of the topological ($\equiv$ twisted $N=2$) algebra captures the ‘invariant’ content of two-dimensional gravity coupled to matter.The topological algebra allows reductions to either the DDK-dressed matter or the ‘Kontsevich-Miwa’-dressed matter related to Virasoro-constrained KP hierarchy. The standard DDK formulation is recovered by splitting the topological generators into $c=-26$ reparametrization ghosts + matter + ‘Liouville’, while a similar splitting involving $c=-2$ ghosts gives rise to the matter dressed in exactly the way required in order that the theory be equivalent to Virasoro constraints on the KP hierarchy. The two dressings of matter with the ‘Liouville’ differ also by their ‘ghost numbers’, which is similar to the existence of representatives of BRST cohomologies with different ghost numbers. The topological central $c\ne 3$ provides a two-fold covering of the allowed region $d\le 1\cup d\ge 25$ of the matter central charge $d$ via $d+(c+1)(c+6)(c-3)$. The ‘Liouville’ field is identified as the ghost-free part of the topological $U(1)$ current. The construction thus allows one to establish a direct relation (presumably an equivalence) between the Virasoro-constrained KP hierarchies, minimal models, and the BRST invariance condition for highest-weight states of the topological algebra. 
@article{TMF_1993_95_2_a8,
     author = {B. Gato-Rivera and A. M. Semikhatov},
     title = {$d\le 1\cup d\ge 25$ and constrained {KP} hierarchy from {BRST} invariance in the $c\ne 3$ topological algebra},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {239--250},
     year = {1993},
     volume = {95},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_95_2_a8/}
}
TY  - JOUR
AU  - B. Gato-Rivera
AU  - A. M. Semikhatov
TI  - $d\le 1\cup d\ge 25$ and constrained KP hierarchy from BRST invariance in the $c\ne 3$ topological algebra
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1993
SP  - 239
EP  - 250
VL  - 95
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1993_95_2_a8/
LA  - ru
ID  - TMF_1993_95_2_a8
ER  - 
%0 Journal Article
%A B. Gato-Rivera
%A A. M. Semikhatov
%T $d\le 1\cup d\ge 25$ and constrained KP hierarchy from BRST invariance in the $c\ne 3$ topological algebra
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1993
%P 239-250
%V 95
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1993_95_2_a8/
%G ru
%F TMF_1993_95_2_a8
B. Gato-Rivera; A. M. Semikhatov. $d\le 1\cup d\ge 25$ and constrained KP hierarchy from BRST invariance in the $c\ne 3$ topological algebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 2, pp. 239-250. http://geodesic.mathdoc.fr/item/TMF_1993_95_2_a8/

[1] Brézin E., Kazakov V. A., Phys. Lett., B236 (1990), 144 | DOI | MR

[2] Douglas M. R., Shenker S. H., Nucl. Phys., B335 (1990), 635 | DOI | MR | Zbl

[3] Gross D. J., Migdal A. A., Phys. Rev. Lett., 64 (1990), 127 | DOI | MR | Zbl

[4] Douglas M. R., Phys. Lett., B238 (1990), 176 | DOI | MR | Zbl

[5] Fukuma M., Kawai H., Nakayama R., Int. J. Mod. Phys., A6 (1991), 1385 ; Explicit Solution for $p-q$ Duality in Two-Dimensional Quantum Gravity, Univ. Tokyo preprint UT-582, may 1991 | DOI | MR | Zbl

[6] Dijkgraaf R., Verlinde E., Verlinde H., Nucl. Phys., B348 (1991), 435 | DOI | MR

[7] Knizhnik V. G., Polyakov A. M., Zamolodchikov A. B., Mod. Phys. Lett., A3 (1988), 819 | DOI | MR

[8] David F., Mod. Phys. Lett., A3 (1988), 1651 | DOI | MR | Zbl

[9] Distler J., Kawai H., Nucl. Phys., B321 (1989), 509 | DOI | MR

[10] Semikhatov A. M., Solving Virasoro Constraints on Integrable Hierarchies via the Kontsevich-Miwa Transform, ; Gato-Rivera B., Semikhatov A. M., “Singular vectors and topological theories from Virasoro constraints via the Kontsevich-Miwa transform”, Nuclear Phys. B, 408:1 (1993), 133–179 arXiv:9204063v1.pdf | MR | DOI | MR | Zbl

[11] Gato-Rivera B., Semikhatov A. M., Phys. Lett., B288 (1992), 38 | DOI | MR

[12] Konisevich M., Funk. An. Prilozh., 25:2 (1991), 50

[13] Witten E., On the Konsevich Model and Other Models of Two-Dimensional Gravity, Princeton preprint IASSNS-HEP-91-24, july 1991 | MR

[14] Makeenko Yu., Semenoff G., Properties of Hermitian Matrix Model in External Field, British Columbia Univ. prepr. 91-0329, july 1991 | MR

[15] Kharchev S., Marshakov A., Mironov A., Morozov A., Zabrodin A., Towards Unified Theory of Quantum Gravity, Lebedev Inst. preprint FIAN-TD-03-92, oct. 1991 | MR

[16] Gross D. J., Newman M. J., Unitary and Hermitean Matrices in an External. II: The Kontsevich Model and Continuum Virasoro Constraints, princeton preprint PUPT-1282, 1991 | MR

[17] Witten E., Commun. Math. Phys., 118 (1988), 411 ; Nucl. Phys., B340 (1990), 281 | DOI | MR | Zbl | DOI | MR

[18] Eguchi T., Yang S.-K., Mod. Phys. Lett., A4 (1990), 1653 | MR

[19] Belavin A. A., Polyakov A. M., Zamolodchikov A. B., Nucl. Phys., B241 (1984), 333 | DOI | MR | Zbl

[20] Friedan D., Qiu Z., Shenker S., Phys. Rev. Lett., 52 (1984), 1575 | DOI | MR

[21] Dotsenko Vl. S., Fateev V. A., Nucl. Phys., B240 (1984), 312 | DOI | MR

[22] Witten E., Nucl. Phys., B340 (1990), 281 | DOI | MR

[23] Dijkgraaf R., Witten E., Nucl. Phys., B342 (1991), 486 | MR

[24] Verlinde E., Verlinde H., Nucl. Phys., B348 (1991), 457 | DOI | MR

[25] Martinec E., Phys. Lett., B217 (1989), 431 | DOI | MR

[26] Vafa C., Warner N. P., Phys. Lett., B218 (1989), 51 | DOI | MR

[27] Witten E., Nucl. Phys., B373 (1992), 187 | DOI | MR

[28] Kutasov D., Martinec E., Seiberg N., Phys. Lett., B276 (1992), 437 | DOI | MR

[29] Lian B., Zuckerman G., Phys. Lett., B254 (1991), 417 | DOI | MR | Zbl

[30] Miwa T., Proc. Japan Acad. Sci., 58 (1982), 9 | DOI | MR | Zbl

[31] Saito S., Phys. Rev., D36 (1987), 1819 | MR

[32] Distler J., Nucl. Phys., B324 (1990), 523 | DOI | MR

[33] Semikhatov A. M., Int. J. Mod. Phys., A4 (1989), 467 | DOI | MR | Zbl

[34] Grinevich P. G., Orlov A. Yu., Flag spaces in KP Theory and Virasoro action on $\det\overline {\partial}_j$ and Segal-Wilson Tau Function, Cornell Univ. prepr. CLNS 89/945

[35] Lerche W., Vafa C., Warner N. P., Nucl. Phys., B324 (1989), 427 | DOI | MR

[36] Gato-Rivera B., Semikhatov A. M., “Singular vectors and topological theories from Virasoro constraints via the Kontsevich-Miwa transform”, Nuclear Phys. B, 408:1 (1993), 133–179 | DOI | MR | Zbl

[37] Friedan D. H., Martinec E. J., Shenker S. H., Nucl. Phys., B271 (1986), 93 | DOI | MR

[38] Semikhatov A. M., Nucl. Phys., B366 (1991), 347 | DOI | MR

[39] Vafa C., Mod. Phys. Lett., A6 (1991), 337 | DOI | MR | Zbl