Geodesic
The~сigar soliton and the~Ricci flows perturbation solutions in the~two-dimensional string $\sigma$ model
Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 1, pp. 97-110

Voir la notice de l'article provenant de la source Math-Net.Ru

The Ricci flows perturbation equations and the Weyl anomaly coefficients are derived in the two-dimensional bosonic string $\sigma$ model. These equations correspond to the two-loop flow equations for the graviton field $g_{\mu\nu}$ and the dilaton field $\Phi$. The one-loop perturbation solution of the cigar soliton can be expressed in terms of the hypergeometric functions. The two-loop asymptotic perturbation solution of the cigar soliton is reduced by using a small parameter expansion method. Moreover, analytic solutions of the second basic form $l$ and $n$ are obtained in accordance with the perturbation Gauss–Codazzi equations. The modified expression of the deformed principal curvatures of a two-dimensional surface can then be given in terms of $l$ and $n$. The influence of quantum Ricci flows on the space–time geometry is analyzed and discussed, and the physical meaning of the Weyl anomaly coefficients varying with the momentum scale $\lambda$ is also explained.
Mots-clés : cigar soliton, perturbation solutions
Keywords: Ricci flows, two-dimensional string $\sigma$ model. 
@article{TMF_2023_215_1_a4,
     author = {Jun Yan},
     title = {The~{\cyrs}igar soliton and {the~Ricci} flows perturbation solutions in the~two-dimensional string $\sigma$ model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {97--110},
     publisher = {mathdoc},
     volume = {215},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_215_1_a4/}
}
TY  - JOUR
AU  - Jun Yan
TI  - The~сigar soliton and the~Ricci flows perturbation solutions in the~two-dimensional string $\sigma$ model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 97
EP  - 110
VL  - 215
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_215_1_a4/
LA  - ru
ID  - TMF_2023_215_1_a4
ER  - 
%0 Journal Article
%A Jun Yan
%T The~сigar soliton and the~Ricci flows perturbation solutions in the~two-dimensional string $\sigma$ model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 97-110
%V 215
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2023_215_1_a4/
%G ru
%F TMF_2023_215_1_a4
Jun Yan. The~сigar soliton and the~Ricci flows perturbation solutions in the~two-dimensional string $\sigma$ model. Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 1, pp. 97-110. http://geodesic.mathdoc.fr/item/TMF_2023_215_1_a4/