1994/06/19 by I. L. Buchbinder, Buchbinder, I. L., I. L. Shapiro +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9406127
30 pages
arxiv created 1994/06/19 · openalex publication_date 1994/06/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The unified theory of string and two-dimensional quantum gravity is considered. The action for two-dimensional gravity is choosen in a well-known induced form and thus gravity posesses it's oun nontrivial dynamics even on the classical level. Three classically equivalent forms of the action of the unified theory are described, that is D, D+1 and D+2 formulations where the last one corresponds to the special kind of nonlinear sigma model on the background of classical two-dimensional metric. In all cases we find the action of the theory to be invariant under generalized symmetry transformations, and point out the arbitrariness of renormalization which reflects this symmetry. The one - loop counterterms are calculated in a general covariant gauge and also in conformal gauge. The difference between the counterterms for all classically equivalent variants of the theory is trivial on mass-shell. Since the different versions of the theory lead to the one-loop contributions which coincide on mass shell, the corresponding arbitrariness is related with the only generalized reparametrizations of the theory. Hence one can formulate the conditions of Weyl symmetry for any equivalent form of the action. Such a conditions are written for the D+2 formulation and then are reduced to other ones. The equations for the background interaction fields differ from the ones in standard approach and look much more complicated.