arXiv subjects
Publications and source records attributed to A. M. Polyakov.
We study the gravitational dressing of renormalizable two-dimensional field theories. Our main result is that the one-loop $β$-function is finitely renormalized by the factor ${k+2\over k+1}$, where $k$ is the central charge of the gravitational $SL(2, R)$ current algebra.
In these lectures I discuss various unsolved problems of string theory and their relations to quantum gravity, 3d Ising model, large N QCD, and quantum cosmology. No solutions are presented but some new and perhaps useful approaches are suggested.
The methods of conformal field theory are used to obtain the series of exact solutions of the fundamental equations of the theory of turbulence. The basic conjecture, proved to be self-consistent ,is the conformal invariance of the inertial range. The resulting physical picture is different from the standard one , since the enstrophy transfer is catalyzed by the large scale motions. The theory gives some unambiguous predictions for the correlations in the inertial range.
We study the couplings of discrete states that appear in the string theory embedded in two dimensions, and show that they are given by the structure constants of the group of area preserving diffeomorphisms. We propose an effective action for these states, which is itself invariant under this infinite-dimensional group.